Result for Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, H

Specification

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \end{array} \]

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

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 * 3.0d0))) + (t / ((z * 3.0d0) * y))
end function

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)))
end

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
end

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\begin{array}{l}

\\
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
\end{array}

Sampling outcomes in binary64 precision:

Initial Program: 95.6% accurate, 1.0× speedup?

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \end{array} \]

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

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 * 3.0d0))) + (t / ((z * 3.0d0) * y))
end function

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)))
end

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
end

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\begin{array}{l}

\\
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
\end{array}

Alternative 1: 97.6% accurate, 0.5× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{if}\;t\_1 \leq 10^{+288}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{t}{y} - y}{z}, 0.3333333333333333, x\right)\\ \end{array} \end{array} \]

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y)))))
   (if (<= t_1 1e+288) t_1 (fma (/ (- (/ t y) y) z) 0.3333333333333333 x))))

double code(double x, double y, double z, double t) {
	double t_1 = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	double tmp;
	if (t_1 <= 1e+288) {
		tmp = t_1;
	} else {
		tmp = fma((((t / y) - y) / z), 0.3333333333333333, x);
	}
	return tmp;
}

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)))
	tmp = 0.0
	if (t_1 <= 1e+288)
		tmp = t_1;
	else
		tmp = fma(Float64(Float64(Float64(t / y) - y) / z), 0.3333333333333333, x);
	end
	return tmp
end

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+288], t$95$1, N[(N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision] * 0.3333333333333333 + x), $MachinePrecision]]]

\begin{array}{l}

\\
\begin{array}{l}
t_1 := \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\
\mathbf{if}\;t\_1 \leq 10^{+288}:\\
\;\;\;\;t\_1\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(\frac{\frac{t}{y} - y}{z}, 0.3333333333333333, x\right)\\


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y))) < 1e288
1. Initial program 98.4%
  \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Add Preprocessing
if 1e288 < (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y)))
1. Initial program 88.0%
  \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Add Preprocessing
3. Taylor expanded in x around 0
  \[\leadsto \color{blue}{\left(x + \frac{1}{3} \cdot \frac{t}{y \cdot z}\right) - \frac{1}{3} \cdot \frac{y}{z}} \]
4. Step-by-step derivation
  1. associate--l+N/A
    \[\leadsto x + \color{blue}{\left(\frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z}\right)} \]
  2. distribute-lft-out--N/A
    \[\leadsto x + \frac{1}{3} \cdot \color{blue}{\left(\frac{t}{y \cdot z} - \frac{y}{z}\right)} \]
  3. fp-cancel-sign-sub-invN/A
    \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \left(\frac{t}{y \cdot z} - \frac{y}{z}\right)} \]
  4. metadata-evalN/A
    \[\leadsto x - \frac{-1}{3} \cdot \left(\color{blue}{\frac{t}{y \cdot z}} - \frac{y}{z}\right) \]
  5. associate-/r*N/A
    \[\leadsto x - \frac{-1}{3} \cdot \left(\frac{\frac{t}{y}}{z} - \frac{\color{blue}{y}}{z}\right) \]
  6. sub-divN/A
    \[\leadsto x - \frac{-1}{3} \cdot \frac{\frac{t}{y} - y}{\color{blue}{z}} \]
  7. associate-/l*N/A
    \[\leadsto x - \frac{\frac{-1}{3} \cdot \left(\frac{t}{y} - y\right)}{\color{blue}{z}} \]
  8. distribute-lft-out--N/A
    \[\leadsto x - \frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z} \]
  9. *-lft-identityN/A
    \[\leadsto x - 1 \cdot \color{blue}{\frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z}} \]
  10. fp-cancel-sub-sign-invN/A
    \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z}} \]
  11. metadata-evalN/A
    \[\leadsto x + -1 \cdot \frac{\color{blue}{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}}{z} \]
  12. +-commutativeN/A
    \[\leadsto -1 \cdot \frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z} + \color{blue}{x} \]
5. Applied rewrites99.9%
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{t}{y} - y}{z}, 0.3333333333333333, x\right)} \]
Recombined 2 regimes into one program.
Add Preprocessing

Alternative 2: 96.2% accurate, 0.9× speedup?

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z}}{3 \cdot y} \end{array} \]

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ (/ t z) (* 3.0 y))))

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / z) / (3.0 * y));
}

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 * 3.0d0))) + ((t / z) / (3.0d0 * y))
end function

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / z) / (3.0 * y));
}

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + ((t / z) / (3.0 * y))

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(Float64(t / z) / Float64(3.0 * y)))
end

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + ((t / z) / (3.0 * y));
end

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t / z), $MachinePrecision] / N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\begin{array}{l}

\\
\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z}}{3 \cdot y}
\end{array}

Derivation

Initial program 96.5%
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
Add Preprocessing
Step-by-step derivation
1. lift-/.f64N/A
  \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}} \]
2. lift-*.f64N/A
  \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right)} \cdot y} \]
3. lift-*.f64N/A
  \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]
4. associate-*l*N/A
  \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]
5. associate-/r*N/A
  \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z}}{3 \cdot y}} \]
6. lower-/.f64N/A
  \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z}}{3 \cdot y}} \]
7. lower-/.f64N/A
  \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\frac{t}{z}}}{3 \cdot y} \]
8. lower-*.f6498.0
  \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z}}{\color{blue}{3 \cdot y}} \]
Applied rewrites98.0%
\[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z}}{3 \cdot y}} \]
Add Preprocessing

Alternative 3: 89.9% accurate, 1.2× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+20} \lor \neg \left(y \leq 3.5 \cdot 10^{+58}\right):\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array} \end{array} \]

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.1e+20) (not (<= y 3.5e+58)))
   (fma -0.3333333333333333 (/ y z) x)
   (+ x (/ t (* (* z 3.0) y)))))

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.1e+20) || !(y <= 3.5e+58)) {
		tmp = fma(-0.3333333333333333, (y / z), x);
	} else {
		tmp = x + (t / ((z * 3.0) * y));
	}
	return tmp;
}

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.1e+20) || !(y <= 3.5e+58))
		tmp = fma(-0.3333333333333333, Float64(y / z), x);
	else
		tmp = Float64(x + Float64(t / Float64(Float64(z * 3.0) * y)));
	end
	return tmp
end

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.1e+20], N[Not[LessEqual[y, 3.5e+58]], $MachinePrecision]], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;y \leq -1.1 \cdot 10^{+20} \lor \neg \left(y \leq 3.5 \cdot 10^{+58}\right):\\
\;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{t}{\left(z \cdot 3\right) \cdot y}\\


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if y < -1.1e20 or 3.4999999999999997e58 < y
1. Initial program 99.8%
  \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Add Preprocessing
3. Taylor expanded in t around 0
  \[\leadsto \color{blue}{x - \frac{1}{3} \cdot \frac{y}{z}} \]
4. Step-by-step derivation
  1. metadata-evalN/A
    \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{\color{blue}{y}}{z} \]
  2. fp-cancel-sign-sub-invN/A
    \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]
  3. +-commutativeN/A
    \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]
  4. lower-fma.f64N/A
    \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \color{blue}{\frac{y}{z}}, x\right) \]
  5. lower-/.f6495.7
    \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{\color{blue}{z}}, x\right) \]
5. Applied rewrites95.7%
  \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)} \]
if -1.1e20 < y < 3.4999999999999997e58
1. Initial program 93.9%
  \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Add Preprocessing
3. Taylor expanded in x around inf
  \[\leadsto \color{blue}{x} + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
4. Step-by-step derivation
5. Applied rewrites88.0%
  \[\leadsto \color{blue}{x} + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
Recombined 2 regimes into one program.
Final simplification91.3%
\[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+20} \lor \neg \left(y \leq 3.5 \cdot 10^{+58}\right):\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array} \]
Add Preprocessing

Alternative 4: 89.9% accurate, 1.2× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+20} \lor \neg \left(y \leq 3.5 \cdot 10^{+58}\right):\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array} \end{array} \]

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.1e+20) (not (<= y 3.5e+58)))
   (fma -0.3333333333333333 (/ y z) x)
   (+ x (/ t (* z (* 3.0 y))))))

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.1e+20) || !(y <= 3.5e+58)) {
		tmp = fma(-0.3333333333333333, (y / z), x);
	} else {
		tmp = x + (t / (z * (3.0 * y)));
	}
	return tmp;
}

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.1e+20) || !(y <= 3.5e+58))
		tmp = fma(-0.3333333333333333, Float64(y / z), x);
	else
		tmp = Float64(x + Float64(t / Float64(z * Float64(3.0 * y))));
	end
	return tmp
end

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.1e+20], N[Not[LessEqual[y, 3.5e+58]], $MachinePrecision]], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(t / N[(z * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;y \leq -1.1 \cdot 10^{+20} \lor \neg \left(y \leq 3.5 \cdot 10^{+58}\right):\\
\;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{t}{z \cdot \left(3 \cdot y\right)}\\


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if y < -1.1e20 or 3.4999999999999997e58 < y
1. Initial program 99.8%
  \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Add Preprocessing
3. Taylor expanded in t around 0
  \[\leadsto \color{blue}{x - \frac{1}{3} \cdot \frac{y}{z}} \]
4. Step-by-step derivation
  1. metadata-evalN/A
    \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{\color{blue}{y}}{z} \]
  2. fp-cancel-sign-sub-invN/A
    \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]
  3. +-commutativeN/A
    \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]
  4. lower-fma.f64N/A
    \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \color{blue}{\frac{y}{z}}, x\right) \]
  5. lower-/.f6495.7
    \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{\color{blue}{z}}, x\right) \]
5. Applied rewrites95.7%
  \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)} \]
if -1.1e20 < y < 3.4999999999999997e58
1. Initial program 93.9%
  \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Add Preprocessing
3. Taylor expanded in x around inf
  \[\leadsto \color{blue}{x} + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
4. Step-by-step derivation
5. Applied rewrites88.0%
  \[\leadsto \color{blue}{x} + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
6. Step-by-step derivation
  1. lift-*.f64N/A
    \[\leadsto x + \frac{t}{\color{blue}{\left(z \cdot 3\right)} \cdot y} \]
  2. lift-*.f64N/A
    \[\leadsto x + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]
  3. associate-*l*N/A
    \[\leadsto x + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]
  4. lower-*.f64N/A
    \[\leadsto x + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]
  5. lift-*.f6488.0
    \[\leadsto x + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]
7. Applied rewrites88.0%
  \[\leadsto x + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]
Recombined 2 regimes into one program.
Final simplification91.3%
\[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+20} \lor \neg \left(y \leq 3.5 \cdot 10^{+58}\right):\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array} \]
Add Preprocessing

Alternative 5: 89.9% accurate, 1.2× speedup?

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.1e+20) (not (<= y 3.5e+58)))
   (fma -0.3333333333333333 (/ y z) x)
   (+ x (/ t (* (* z y) 3.0)))))

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.1e+20) || !(y <= 3.5e+58)) {
		tmp = fma(-0.3333333333333333, (y / z), x);
	} else {
		tmp = x + (t / ((z * y) * 3.0));
	}
	return tmp;
}

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.1e+20) || !(y <= 3.5e+58))
		tmp = fma(-0.3333333333333333, Float64(y / z), x);
	else
		tmp = Float64(x + Float64(t / Float64(Float64(z * y) * 3.0)));
	end
	return tmp
end

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.1e+20], N[Not[LessEqual[y, 3.5e+58]], $MachinePrecision]], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(t / N[(N[(z * y), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;y \leq -1.1 \cdot 10^{+20} \lor \neg \left(y \leq 3.5 \cdot 10^{+58}\right):\\
\;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{t}{\left(z \cdot y\right) \cdot 3}\\


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if y < -1.1e20 or 3.4999999999999997e58 < y
1. Initial program 99.8%
  \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Add Preprocessing
3. Taylor expanded in t around 0
  \[\leadsto \color{blue}{x - \frac{1}{3} \cdot \frac{y}{z}} \]
4. Step-by-step derivation
  1. metadata-evalN/A
    \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{\color{blue}{y}}{z} \]
  2. fp-cancel-sign-sub-invN/A
    \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]
  3. +-commutativeN/A
    \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]
  4. lower-fma.f64N/A
    \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \color{blue}{\frac{y}{z}}, x\right) \]
  5. lower-/.f6495.7
    \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{\color{blue}{z}}, x\right) \]
5. Applied rewrites95.7%
  \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)} \]
if -1.1e20 < y < 3.4999999999999997e58
1. Initial program 93.9%
  \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Add Preprocessing
3. Taylor expanded in x around inf
  \[\leadsto \color{blue}{x} + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
4. Step-by-step derivation
5. Applied rewrites88.0%
  \[\leadsto \color{blue}{x} + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
6. Taylor expanded in y around 0
  \[\leadsto x + \frac{t}{\color{blue}{3 \cdot \left(y \cdot z\right)}} \]
7. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto x + \frac{t}{\left(y \cdot z\right) \cdot \color{blue}{3}} \]
  2. lower-*.f64N/A
    \[\leadsto x + \frac{t}{\left(y \cdot z\right) \cdot \color{blue}{3}} \]
  3. *-commutativeN/A
    \[\leadsto x + \frac{t}{\left(z \cdot y\right) \cdot 3} \]
  4. lower-*.f6487.9
    \[\leadsto x + \frac{t}{\left(z \cdot y\right) \cdot 3} \]
8. Applied rewrites87.9%
  \[\leadsto x + \frac{t}{\color{blue}{\left(z \cdot y\right) \cdot 3}} \]
Recombined 2 regimes into one program.
Final simplification91.3%
\[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+20} \lor \neg \left(y \leq 3.5 \cdot 10^{+58}\right):\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\left(z \cdot y\right) \cdot 3}\\ \end{array} \]
Add Preprocessing

Alternative 6: 76.4% accurate, 1.3× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-10} \lor \neg \left(y \leq 1.02 \cdot 10^{-45}\right):\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333 \cdot t}{z \cdot y}\\ \end{array} \end{array} \]

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.35e-10) (not (<= y 1.02e-45)))
   (fma -0.3333333333333333 (/ y z) x)
   (/ (* 0.3333333333333333 t) (* z y))))

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.35e-10) || !(y <= 1.02e-45)) {
		tmp = fma(-0.3333333333333333, (y / z), x);
	} else {
		tmp = (0.3333333333333333 * t) / (z * y);
	}
	return tmp;
}

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.35e-10) || !(y <= 1.02e-45))
		tmp = fma(-0.3333333333333333, Float64(y / z), x);
	else
		tmp = Float64(Float64(0.3333333333333333 * t) / Float64(z * y));
	end
	return tmp
end

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.35e-10], N[Not[LessEqual[y, 1.02e-45]], $MachinePrecision]], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision] + x), $MachinePrecision], N[(N[(0.3333333333333333 * t), $MachinePrecision] / N[(z * y), $MachinePrecision]), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;y \leq -2.35 \cdot 10^{-10} \lor \neg \left(y \leq 1.02 \cdot 10^{-45}\right):\\
\;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{0.3333333333333333 \cdot t}{z \cdot y}\\


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if y < -2.3500000000000002e-10 or 1.0199999999999999e-45 < y
1. Initial program 99.8%
  \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Add Preprocessing
3. Taylor expanded in t around 0
  \[\leadsto \color{blue}{x - \frac{1}{3} \cdot \frac{y}{z}} \]
4. Step-by-step derivation
  1. metadata-evalN/A
    \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{\color{blue}{y}}{z} \]
  2. fp-cancel-sign-sub-invN/A
    \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]
  3. +-commutativeN/A
    \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]
  4. lower-fma.f64N/A
    \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \color{blue}{\frac{y}{z}}, x\right) \]
  5. lower-/.f6491.2
    \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{\color{blue}{z}}, x\right) \]
5. Applied rewrites91.2%
  \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)} \]
if -2.3500000000000002e-10 < y < 1.0199999999999999e-45
1. Initial program 92.9%
  \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Add Preprocessing
3. Step-by-step derivation
  1. lift-/.f64N/A
    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}} \]
  2. lift-*.f64N/A
    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right)} \cdot y} \]
  3. lift-*.f64N/A
    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]
  4. associate-*l*N/A
    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]
  5. associate-/r*N/A
    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z}}{3 \cdot y}} \]
  6. lower-/.f64N/A
    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z}}{3 \cdot y}} \]
  7. lower-/.f64N/A
    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\frac{t}{z}}}{3 \cdot y} \]
  8. lower-*.f6496.9
    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z}}{\color{blue}{3 \cdot y}} \]
4. Applied rewrites96.9%
  \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z}}{3 \cdot y}} \]
5. Step-by-step derivation
  1. lift-+.f64N/A
    \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z}}{3 \cdot y}} \]
  2. lift--.f64N/A
    \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right)} + \frac{\frac{t}{z}}{3 \cdot y} \]
  3. lift-*.f64N/A
    \[\leadsto \left(x - \frac{y}{\color{blue}{z \cdot 3}}\right) + \frac{\frac{t}{z}}{3 \cdot y} \]
  4. lift-/.f64N/A
    \[\leadsto \left(x - \color{blue}{\frac{y}{z \cdot 3}}\right) + \frac{\frac{t}{z}}{3 \cdot y} \]
  5. lift-/.f64N/A
    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\frac{t}{z}}}{3 \cdot y} \]
  6. lift-*.f64N/A
    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z}}{\color{blue}{3 \cdot y}} \]
  7. lift-/.f64N/A
    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z}}{3 \cdot y}} \]
  8. associate-+l-N/A
    \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{\frac{t}{z}}{3 \cdot y}\right)} \]
  9. associate-/l/N/A
    \[\leadsto x - \left(\frac{y}{z \cdot 3} - \color{blue}{\frac{t}{z \cdot \left(3 \cdot y\right)}}\right) \]
  10. associate-*l*N/A
    \[\leadsto x - \left(\frac{y}{z \cdot 3} - \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right) \]
  11. lower--.f64N/A
    \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
  12. lower--.f64N/A
    \[\leadsto x - \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
  13. lift-/.f64N/A
    \[\leadsto x - \left(\color{blue}{\frac{y}{z \cdot 3}} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right) \]
  14. *-commutativeN/A
    \[\leadsto x - \left(\frac{y}{\color{blue}{3 \cdot z}} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right) \]
  15. lower-*.f64N/A
    \[\leadsto x - \left(\frac{y}{\color{blue}{3 \cdot z}} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right) \]
  16. lift-*.f64N/A
    \[\leadsto x - \left(\frac{y}{3 \cdot z} - \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right) \]
  17. lift-*.f64N/A
    \[\leadsto x - \left(\frac{y}{3 \cdot z} - \frac{t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right) \]
  18. lift-/.f6492.9
    \[\leadsto x - \left(\frac{y}{3 \cdot z} - \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right) \]
  19. lift-*.f64N/A
    \[\leadsto x - \left(\frac{y}{3 \cdot z} - \frac{t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right) \]
  20. *-commutativeN/A
    \[\leadsto x - \left(\frac{y}{3 \cdot z} - \frac{t}{\color{blue}{\left(3 \cdot z\right)} \cdot y}\right) \]
  21. lower-*.f6492.9
    \[\leadsto x - \left(\frac{y}{3 \cdot z} - \frac{t}{\color{blue}{\left(3 \cdot z\right)} \cdot y}\right) \]
6. Applied rewrites92.9%
  \[\leadsto \color{blue}{x - \left(\frac{y}{3 \cdot z} - \frac{t}{\left(3 \cdot z\right) \cdot y}\right)} \]
7. Taylor expanded in y around 0
  \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{t}{y \cdot z}} \]
8. Step-by-step derivation
  1. associate--r-N/A
    \[\leadsto \color{blue}{\frac{1}{3}} \cdot \frac{t}{y \cdot z} \]
  2. *-commutativeN/A
    \[\leadsto \frac{1}{3} \cdot \frac{t}{y \cdot z} \]
  3. *-commutativeN/A
    \[\leadsto \frac{1}{3} \cdot \frac{t}{y \cdot z} \]
  4. *-commutativeN/A
    \[\leadsto \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]
  5. lower-*.f64N/A
    \[\leadsto \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]
  6. associate-/r*N/A
    \[\leadsto \frac{\frac{t}{y}}{z} \cdot \frac{1}{3} \]
  7. lower-/.f64N/A
    \[\leadsto \frac{\frac{t}{y}}{z} \cdot \frac{1}{3} \]
  8. lift-/.f6460.4
    \[\leadsto \frac{\frac{t}{y}}{z} \cdot 0.3333333333333333 \]
9. Applied rewrites60.4%
  \[\leadsto \color{blue}{\frac{\frac{t}{y}}{z} \cdot 0.3333333333333333} \]
10. Step-by-step derivation
  1. lift-*.f64N/A
    \[\leadsto \frac{\frac{t}{y}}{z} \cdot \color{blue}{\frac{1}{3}} \]
  2. lift-/.f64N/A
    \[\leadsto \frac{\frac{t}{y}}{z} \cdot \frac{1}{3} \]
  3. lift-/.f64N/A
    \[\leadsto \frac{\frac{t}{y}}{z} \cdot \frac{1}{3} \]
  4. *-commutativeN/A
    \[\leadsto \frac{1}{3} \cdot \color{blue}{\frac{\frac{t}{y}}{z}} \]
  5. associate-/r*N/A
    \[\leadsto \frac{1}{3} \cdot \frac{t}{\color{blue}{y \cdot z}} \]
  6. associate-*r/N/A
    \[\leadsto \frac{\frac{1}{3} \cdot t}{\color{blue}{y \cdot z}} \]
  7. lower-/.f64N/A
    \[\leadsto \frac{\frac{1}{3} \cdot t}{\color{blue}{y \cdot z}} \]
  8. lower-*.f64N/A
    \[\leadsto \frac{\frac{1}{3} \cdot t}{\color{blue}{y} \cdot z} \]
  9. *-commutativeN/A
    \[\leadsto \frac{\frac{1}{3} \cdot t}{z \cdot \color{blue}{y}} \]
  10. lower-*.f6464.3
    \[\leadsto \frac{0.3333333333333333 \cdot t}{z \cdot \color{blue}{y}} \]
11. Applied rewrites64.3%
  \[\leadsto \frac{0.3333333333333333 \cdot t}{\color{blue}{z \cdot y}} \]
Recombined 2 regimes into one program.
Final simplification78.3%
\[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-10} \lor \neg \left(y \leq 1.02 \cdot 10^{-45}\right):\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333 \cdot t}{z \cdot y}\\ \end{array} \]
Add Preprocessing

Alternative 7: 76.4% accurate, 1.3× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-10} \lor \neg \left(y \leq 1.02 \cdot 10^{-45}\right):\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z \cdot y} \cdot 0.3333333333333333\\ \end{array} \end{array} \]

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.35e-10) (not (<= y 1.02e-45)))
   (fma -0.3333333333333333 (/ y z) x)
   (* (/ t (* z y)) 0.3333333333333333)))

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.35e-10) || !(y <= 1.02e-45)) {
		tmp = fma(-0.3333333333333333, (y / z), x);
	} else {
		tmp = (t / (z * y)) * 0.3333333333333333;
	}
	return tmp;
}

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.35e-10) || !(y <= 1.02e-45))
		tmp = fma(-0.3333333333333333, Float64(y / z), x);
	else
		tmp = Float64(Float64(t / Float64(z * y)) * 0.3333333333333333);
	end
	return tmp
end

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.35e-10], N[Not[LessEqual[y, 1.02e-45]], $MachinePrecision]], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision] + x), $MachinePrecision], N[(N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;y \leq -2.35 \cdot 10^{-10} \lor \neg \left(y \leq 1.02 \cdot 10^{-45}\right):\\
\;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{t}{z \cdot y} \cdot 0.3333333333333333\\


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if y < -2.3500000000000002e-10 or 1.0199999999999999e-45 < y
1. Initial program 99.8%
  \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Add Preprocessing
3. Taylor expanded in t around 0
  \[\leadsto \color{blue}{x - \frac{1}{3} \cdot \frac{y}{z}} \]
4. Step-by-step derivation
  1. metadata-evalN/A
    \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{\color{blue}{y}}{z} \]
  2. fp-cancel-sign-sub-invN/A
    \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]
  3. +-commutativeN/A
    \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]
  4. lower-fma.f64N/A
    \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \color{blue}{\frac{y}{z}}, x\right) \]
  5. lower-/.f6491.2
    \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{\color{blue}{z}}, x\right) \]
5. Applied rewrites91.2%
  \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)} \]
if -2.3500000000000002e-10 < y < 1.0199999999999999e-45
1. Initial program 92.9%
  \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Add Preprocessing
3. Taylor expanded in y around 0
  \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{t}{y \cdot z}} \]
4. Step-by-step derivation
  1. *-commutativeN/A
    \[\leadsto \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]
  2. lower-*.f64N/A
    \[\leadsto \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]
  3. lower-/.f64N/A
    \[\leadsto \frac{t}{y \cdot z} \cdot \frac{1}{3} \]
  4. *-commutativeN/A
    \[\leadsto \frac{t}{z \cdot y} \cdot \frac{1}{3} \]
  5. lower-*.f6464.3
    \[\leadsto \frac{t}{z \cdot y} \cdot 0.3333333333333333 \]
5. Applied rewrites64.3%
  \[\leadsto \color{blue}{\frac{t}{z \cdot y} \cdot 0.3333333333333333} \]
Recombined 2 regimes into one program.
Final simplification78.3%
\[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-10} \lor \neg \left(y \leq 1.02 \cdot 10^{-45}\right):\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z \cdot y} \cdot 0.3333333333333333\\ \end{array} \]
Add Preprocessing

Alternative 8: 95.8% accurate, 1.4× speedup?

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{\frac{t}{y} - y}{z}, 0.3333333333333333, x\right) \end{array} \]

(FPCore (x y z t)
 :precision binary64
 (fma (/ (- (/ t y) y) z) 0.3333333333333333 x))

double code(double x, double y, double z, double t) {
	return fma((((t / y) - y) / z), 0.3333333333333333, x);
}

function code(x, y, z, t)
	return fma(Float64(Float64(Float64(t / y) - y) / z), 0.3333333333333333, x)
end

code[x_, y_, z_, t_] := N[(N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision] * 0.3333333333333333 + x), $MachinePrecision]

\begin{array}{l}

\\
\mathsf{fma}\left(\frac{\frac{t}{y} - y}{z}, 0.3333333333333333, x\right)
\end{array}

Derivation

Initial program 96.5%
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
Add Preprocessing
Taylor expanded in x around 0
\[\leadsto \color{blue}{\left(x + \frac{1}{3} \cdot \frac{t}{y \cdot z}\right) - \frac{1}{3} \cdot \frac{y}{z}} \]
Step-by-step derivation
1. associate--l+N/A
  \[\leadsto x + \color{blue}{\left(\frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z}\right)} \]
2. distribute-lft-out--N/A
  \[\leadsto x + \frac{1}{3} \cdot \color{blue}{\left(\frac{t}{y \cdot z} - \frac{y}{z}\right)} \]
3. fp-cancel-sign-sub-invN/A
  \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \left(\frac{t}{y \cdot z} - \frac{y}{z}\right)} \]
4. metadata-evalN/A
  \[\leadsto x - \frac{-1}{3} \cdot \left(\color{blue}{\frac{t}{y \cdot z}} - \frac{y}{z}\right) \]
5. associate-/r*N/A
  \[\leadsto x - \frac{-1}{3} \cdot \left(\frac{\frac{t}{y}}{z} - \frac{\color{blue}{y}}{z}\right) \]
6. sub-divN/A
  \[\leadsto x - \frac{-1}{3} \cdot \frac{\frac{t}{y} - y}{\color{blue}{z}} \]
7. associate-/l*N/A
  \[\leadsto x - \frac{\frac{-1}{3} \cdot \left(\frac{t}{y} - y\right)}{\color{blue}{z}} \]
8. distribute-lft-out--N/A
  \[\leadsto x - \frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z} \]
9. *-lft-identityN/A
  \[\leadsto x - 1 \cdot \color{blue}{\frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z}} \]
10. fp-cancel-sub-sign-invN/A
  \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z}} \]
11. metadata-evalN/A
  \[\leadsto x + -1 \cdot \frac{\color{blue}{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}}{z} \]
12. +-commutativeN/A
  \[\leadsto -1 \cdot \frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z} + \color{blue}{x} \]
Applied rewrites94.6%
\[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{t}{y} - y}{z}, 0.3333333333333333, x\right)} \]
Add Preprocessing

Alternative 9: 48.5% accurate, 1.5× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -220000 \lor \neg \left(y \leq 1.32 \cdot 10^{+45}\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -220000.0) (not (<= y 1.32e+45)))
   (* -0.3333333333333333 (/ y z))
   x))

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -220000.0) || !(y <= 1.32e+45)) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

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 ((y <= (-220000.0d0)) .or. (.not. (y <= 1.32d+45))) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -220000.0) || !(y <= 1.32e+45)) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

def code(x, y, z, t):
	tmp = 0
	if (y <= -220000.0) or not (y <= 1.32e+45):
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -220000.0) || !(y <= 1.32e+45))
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -220000.0) || ~((y <= 1.32e+45)))
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -220000.0], N[Not[LessEqual[y, 1.32e+45]], $MachinePrecision]], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;y \leq -220000 \lor \neg \left(y \leq 1.32 \cdot 10^{+45}\right):\\
\;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\

\mathbf{else}:\\
\;\;\;\;x\\


\end{array}
\end{array}

Derivation

Split input into 2 regimes
if y < -2.2e5 or 1.32000000000000005e45 < y
1. Initial program 99.8%
  \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Add Preprocessing
3. Taylor expanded in y around inf
  \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]
4. Step-by-step derivation
  1. lower-*.f64N/A
    \[\leadsto \frac{-1}{3} \cdot \color{blue}{\frac{y}{z}} \]
  2. lower-/.f6473.3
    \[\leadsto -0.3333333333333333 \cdot \frac{y}{\color{blue}{z}} \]
5. Applied rewrites73.3%
  \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
if -2.2e5 < y < 1.32000000000000005e45
1. Initial program 93.6%
  \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Add Preprocessing
3. Taylor expanded in x around inf
  \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation
5. Applied rewrites33.2%
  \[\leadsto \color{blue}{x} \]
Recombined 2 regimes into one program.
Final simplification51.7%
\[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -220000 \lor \neg \left(y \leq 1.32 \cdot 10^{+45}\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Add Preprocessing

Alternative 10: 64.0% accurate, 2.4× speedup?

\[\begin{array}{l} \\ \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right) \end{array} \]

(FPCore (x y z t) :precision binary64 (fma -0.3333333333333333 (/ y z) x))

double code(double x, double y, double z, double t) {
	return fma(-0.3333333333333333, (y / z), x);
}

function code(x, y, z, t)
	return fma(-0.3333333333333333, Float64(y / z), x)
end

code[x_, y_, z_, t_] := N[(-0.3333333333333333 * N[(y / z), $MachinePrecision] + x), $MachinePrecision]

\begin{array}{l}

\\
\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)
\end{array}

Derivation

Initial program 96.5%
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
Add Preprocessing
Taylor expanded in t around 0
\[\leadsto \color{blue}{x - \frac{1}{3} \cdot \frac{y}{z}} \]
Step-by-step derivation
1. metadata-evalN/A
  \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{\color{blue}{y}}{z} \]
2. fp-cancel-sign-sub-invN/A
  \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]
3. +-commutativeN/A
  \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]
4. lower-fma.f64N/A
  \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \color{blue}{\frac{y}{z}}, x\right) \]
5. lower-/.f6463.1
  \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{\color{blue}{z}}, x\right) \]
Applied rewrites63.1%
\[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)} \]
Add Preprocessing

Alternative 11: 30.4% accurate, 44.0× speedup?

\[\begin{array}{l} \\ x \end{array} \]

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

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

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
end function

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

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

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

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

code[x_, y_, z_, t_] := x

\begin{array}{l}

\\
x
\end{array}

Derivation

Initial program 96.5%
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
Add Preprocessing
Taylor expanded in x around inf
\[\leadsto \color{blue}{x} \]
Step-by-step derivation
Applied rewrites28.0%
\[\leadsto \color{blue}{x} \]
Add Preprocessing

Developer Target 1: 96.2% accurate, 0.9× speedup?

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y} \end{array} \]

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y)))

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
}

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 * 3.0d0))) + ((t / (z * 3.0d0)) / y)
end function

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
}

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y)

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(Float64(t / Float64(z * 3.0)) / y))
end

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
end

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

\begin{array}{l}

\\
\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}
\end{array}

Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, H

28.1% of points produce a very large (infinite) output. You may want to add a precondition. (more)

Specification

Local Percentage Accuracy vs ?

Accuracy vs Speed?

Initial Program: 95.6% accurate, 1.0× speedup?

Alternative 1: 97.6% accurate, 0.5× speedup?

`if (+.f64 (-.f64 x (/.f64 y (.f64 z #s(literal 3 binary64)))) (/.f64 t (.f64 (*.f64 z #s(literal 3 binary64)) y))) < 1e288`

`if 1e288 < (+.f64 (-.f64 x (/.f64 y (.f64 z #s(literal 3 binary64)))) (/.f64 t (.f64 (*.f64 z #s(literal 3 binary64)) y)))`

Alternative 2: 96.2% accurate, 0.9× speedup?

Alternative 3: 89.9% accurate, 1.2× speedup?

`if y < -1.1e20 or 3.4999999999999997e58 < y`

`if -1.1e20 < y < 3.4999999999999997e58`

Alternative 4: 89.9% accurate, 1.2× speedup?

`if y < -1.1e20 or 3.4999999999999997e58 < y`

`if -1.1e20 < y < 3.4999999999999997e58`

Alternative 5: 89.9% accurate, 1.2× speedup?

`if y < -1.1e20 or 3.4999999999999997e58 < y`

`if -1.1e20 < y < 3.4999999999999997e58`

Alternative 6: 76.4% accurate, 1.3× speedup?

`if y < -2.3500000000000002e-10 or 1.0199999999999999e-45 < y`

`if -2.3500000000000002e-10 < y < 1.0199999999999999e-45`

Alternative 7: 76.4% accurate, 1.3× speedup?

`if y < -2.3500000000000002e-10 or 1.0199999999999999e-45 < y`

`if -2.3500000000000002e-10 < y < 1.0199999999999999e-45`

Alternative 8: 95.8% accurate, 1.4× speedup?

Alternative 9: 48.5% accurate, 1.5× speedup?

`if y < -2.2e5 or 1.32000000000000005e45 < y`

`if -2.2e5 < y < 1.32000000000000005e45`

Alternative 10: 64.0% accurate, 2.4× speedup?

Alternative 11: 30.4% accurate, 44.0× speedup?

Developer Target 1: 96.2% accurate, 0.9× speedup?

Reproduce

28.1% of points produce a very large (infinite) output. You may want to add a precondition. (more)

Specification

Local Percentage Accuracy vs ?

Accuracy vs Speed?

Initial Program: 95.6% accurate, 1.0× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

Alternative 1: 97.6% accurate, 0.5× speedupMathFPCoreCJuliaWolframTeX?

if (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y))) < 1e288

if 1e288 < (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y)))

Alternative 2: 96.2% accurate, 0.9× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

Alternative 3: 89.9% accurate, 1.2× speedupMathFPCoreCJuliaWolframTeX?

if y < -1.1e20 or 3.4999999999999997e58 < y

if -1.1e20 < y < 3.4999999999999997e58

Alternative 4: 89.9% accurate, 1.2× speedupMathFPCoreCJuliaWolframTeX?

if y < -1.1e20 or 3.4999999999999997e58 < y

if -1.1e20 < y < 3.4999999999999997e58

Alternative 5: 89.9% accurate, 1.2× speedupMathFPCoreCJuliaWolframTeX?

if y < -1.1e20 or 3.4999999999999997e58 < y

if -1.1e20 < y < 3.4999999999999997e58

Alternative 6: 76.4% accurate, 1.3× speedupMathFPCoreCJuliaWolframTeX?

if y < -2.3500000000000002e-10 or 1.0199999999999999e-45 < y

if -2.3500000000000002e-10 < y < 1.0199999999999999e-45

Alternative 7: 76.4% accurate, 1.3× speedupMathFPCoreCJuliaWolframTeX?

if y < -2.3500000000000002e-10 or 1.0199999999999999e-45 < y

if -2.3500000000000002e-10 < y < 1.0199999999999999e-45

Alternative 8: 95.8% accurate, 1.4× speedupMathFPCoreCJuliaWolframTeX?

Alternative 9: 48.5% accurate, 1.5× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

if y < -2.2e5 or 1.32000000000000005e45 < y

if -2.2e5 < y < 1.32000000000000005e45

Alternative 10: 64.0% accurate, 2.4× speedupMathFPCoreCJuliaWolframTeX?

Alternative 11: 30.4% accurate, 44.0× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

Developer Target 1: 96.2% accurate, 0.9× speedupMathFPCoreCFortranJavaPythonJuliaMATLABWolframTeX?

Reproduce

Initial Program: 95.6% accurate, 1.0× speedup?

Alternative 1: 97.6% accurate, 0.5× speedup?

`if (+.f64 (-.f64 x (/.f64 y (.f64 z #s(literal 3 binary64)))) (/.f64 t (.f64 (*.f64 z #s(literal 3 binary64)) y))) < 1e288`

`if 1e288 < (+.f64 (-.f64 x (/.f64 y (.f64 z #s(literal 3 binary64)))) (/.f64 t (.f64 (*.f64 z #s(literal 3 binary64)) y)))`

Alternative 2: 96.2% accurate, 0.9× speedup?

Alternative 3: 89.9% accurate, 1.2× speedup?

`if y < -1.1e20 or 3.4999999999999997e58 < y`

`if -1.1e20 < y < 3.4999999999999997e58`

Alternative 4: 89.9% accurate, 1.2× speedup?

`if y < -1.1e20 or 3.4999999999999997e58 < y`

`if -1.1e20 < y < 3.4999999999999997e58`

Alternative 5: 89.9% accurate, 1.2× speedup?

`if y < -1.1e20 or 3.4999999999999997e58 < y`

`if -1.1e20 < y < 3.4999999999999997e58`

Alternative 6: 76.4% accurate, 1.3× speedup?

`if y < -2.3500000000000002e-10 or 1.0199999999999999e-45 < y`

`if -2.3500000000000002e-10 < y < 1.0199999999999999e-45`

Alternative 7: 76.4% accurate, 1.3× speedup?

`if y < -2.3500000000000002e-10 or 1.0199999999999999e-45 < y`

`if -2.3500000000000002e-10 < y < 1.0199999999999999e-45`

Alternative 8: 95.8% accurate, 1.4× speedup?

Alternative 9: 48.5% accurate, 1.5× speedup?

`if y < -2.2e5 or 1.32000000000000005e45 < y`

`if -2.2e5 < y < 1.32000000000000005e45`

Alternative 10: 64.0% accurate, 2.4× speedup?

Alternative 11: 30.4% accurate, 44.0× speedup?

Developer Target 1: 96.2% accurate, 0.9× speedup?