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

Percentage Accurate: 96.0% → 98.2%

Time: 4.0s

Alternatives: 13

Speedup: 0.8×

• 28.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * 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 = (x - (y / (z * 3.0d0))) + (t / ((z * 3.0d0) * y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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]

Initial Program: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * 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 = (x - (y / (z * 3.0d0))) + (t / ((z * 3.0d0) * y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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]

Alternative 1: 98.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;t \leq 4.2 \cdot 10^{+36}:\\ \;\;\;\;t\_1 + \frac{\frac{t}{z}}{3 \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ y (* z 3.0)))))
   (if (<= t 4.2e+36)
     (+ t_1 (/ (/ t z) (* 3.0 y)))
     (+ t_1 (/ t (* (* z 3.0) y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y / (z * 3.0));
	double tmp;
	if (t <= 4.2e+36) {
		tmp = t_1 + ((t / z) / (3.0 * y));
	} else {
		tmp = t_1 + (t / ((z * 3.0) * y));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y / (z * 3.0d0))
    if (t <= 4.2d+36) then
        tmp = t_1 + ((t / z) / (3.0d0 * y))
    else
        tmp = t_1 + (t / ((z * 3.0d0) * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (y / (z * 3.0));
	double tmp;
	if (t <= 4.2e+36) {
		tmp = t_1 + ((t / z) / (3.0 * y));
	} else {
		tmp = t_1 + (t / ((z * 3.0) * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y / (z * 3.0))
	tmp = 0
	if t <= 4.2e+36:
		tmp = t_1 + ((t / z) / (3.0 * y))
	else:
		tmp = t_1 + (t / ((z * 3.0) * y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y / Float64(z * 3.0)))
	tmp = 0.0
	if (t <= 4.2e+36)
		tmp = Float64(t_1 + Float64(Float64(t / z) / Float64(3.0 * y)));
	else
		tmp = Float64(t_1 + Float64(t / Float64(Float64(z * 3.0) * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y / (z * 3.0));
	tmp = 0.0;
	if (t <= 4.2e+36)
		tmp = t_1 + ((t / z) / (3.0 * y));
	else
		tmp = t_1 + (t / ((z * 3.0) * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 4.2e+36], N[(t$95$1 + N[(N[(t / z), $MachinePrecision] / N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < 4.20000000000000009e36

   1. Initial program 94.7%

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

      1. lift-/.f64 N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right)} \cdot y} \]

      3. lift-*.f64 N/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-/.f64 N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z}}{3 \cdot y}} \]

      7. lower-/.f64 N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\frac{t}{z}}}{3 \cdot y} \]

      8. lower-*.f64 99.3

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z}}{\color{blue}{3 \cdot y}} \]

   4. Applied rewrites 99.3%

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z}}{3 \cdot y}} \]

   if 4.20000000000000009e36 < t

   1. Initial program 98.1%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 90.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{0.3333333333333333 \cdot y}{z}\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.2:\\ \;\;\;\;x + \frac{\frac{t}{3 \cdot z}}{y}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+111}:\\ \;\;\;\;\left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ (* 0.3333333333333333 y) z))))
   (if (<= y -6.4e+15)
     t_1
     (if (<= y 6.2)
       (+ x (/ (/ t (* 3.0 z)) y))
       (if (<= y 1.5e+111) (* (- (/ t y) y) (/ 0.3333333333333333 z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - ((0.3333333333333333 * y) / z);
	double tmp;
	if (y <= -6.4e+15) {
		tmp = t_1;
	} else if (y <= 6.2) {
		tmp = x + ((t / (3.0 * z)) / y);
	} else if (y <= 1.5e+111) {
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	} 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 - ((0.3333333333333333d0 * y) / z)
    if (y <= (-6.4d+15)) then
        tmp = t_1
    else if (y <= 6.2d0) then
        tmp = x + ((t / (3.0d0 * z)) / y)
    else if (y <= 1.5d+111) then
        tmp = ((t / y) - y) * (0.3333333333333333d0 / z)
    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 - ((0.3333333333333333 * y) / z);
	double tmp;
	if (y <= -6.4e+15) {
		tmp = t_1;
	} else if (y <= 6.2) {
		tmp = x + ((t / (3.0 * z)) / y);
	} else if (y <= 1.5e+111) {
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - ((0.3333333333333333 * y) / z)
	tmp = 0
	if y <= -6.4e+15:
		tmp = t_1
	elif y <= 6.2:
		tmp = x + ((t / (3.0 * z)) / y)
	elif y <= 1.5e+111:
		tmp = ((t / y) - y) * (0.3333333333333333 / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(Float64(0.3333333333333333 * y) / z))
	tmp = 0.0
	if (y <= -6.4e+15)
		tmp = t_1;
	elseif (y <= 6.2)
		tmp = Float64(x + Float64(Float64(t / Float64(3.0 * z)) / y));
	elseif (y <= 1.5e+111)
		tmp = Float64(Float64(Float64(t / y) - y) * Float64(0.3333333333333333 / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - ((0.3333333333333333 * y) / z);
	tmp = 0.0;
	if (y <= -6.4e+15)
		tmp = t_1;
	elseif (y <= 6.2)
		tmp = x + ((t / (3.0 * z)) / y);
	elseif (y <= 1.5e+111)
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(N[(0.3333333333333333 * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.4e+15], t$95$1, If[LessEqual[y, 6.2], N[(x + N[(N[(t / N[(3.0 * z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+111], N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.4e15 or 1.5e111 < y

   1. Initial program 98.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x - \frac{1}{3} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{\color{blue}{y}}{z} \]

      2. fp-cancel-sign-sub-inv N/A

         \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

      3. +-commutative N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \color{blue}{\frac{y}{z}}, x\right) \]

      5. lower-/.f64 95.5

         \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{\color{blue}{z}}, x\right) \]

   5. Applied rewrites 95.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \frac{y}{\color{blue}{z}}, x\right) \]

      2. lift-fma.f64 N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

      3. +-commutative N/A

         \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

      4. fp-cancel-sign-sub-inv N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{y}{z}} \]

      5. metadata-eval N/A

         \[\leadsto x - \frac{1}{3} \cdot \frac{\color{blue}{y}}{z} \]

      6. lower--.f64 N/A

         \[\leadsto x - \color{blue}{\frac{1}{3} \cdot \frac{y}{z}} \]

      7. *-commutative N/A

         \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

      8. lower-*.f64 N/A

         \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

      9. lift-/.f64 95.5

         \[\leadsto x - \frac{y}{z} \cdot 0.3333333333333333 \]

   7. Applied rewrites 95.5%

      \[\leadsto x - \color{blue}{\frac{y}{z} \cdot 0.3333333333333333} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

      2. lift-/.f64 N/A

         \[\leadsto x - \frac{y}{z} \cdot \frac{1}{3} \]

      3. *-commutative N/A

         \[\leadsto x - \frac{1}{3} \cdot \color{blue}{\frac{y}{z}} \]

      4. associate-*r/ N/A

         \[\leadsto x - \frac{\frac{1}{3} \cdot y}{\color{blue}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto x - \frac{\frac{1}{3} \cdot y}{\color{blue}{z}} \]

      6. lower-*.f64 95.7

         \[\leadsto x - \frac{0.3333333333333333 \cdot y}{z} \]

   9. Applied rewrites 95.7%

      \[\leadsto x - \frac{0.3333333333333333 \cdot y}{\color{blue}{z}} \]

   if -6.4e15 < y < 6.20000000000000018

   1. Initial program 92.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 87.3%

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

      1. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \frac{t}{\color{blue}{\left(z \cdot 3\right)} \cdot y} \]

      3. lift-*.f64 N/A

         \[\leadsto x + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      4. associate-/r* N/A

         \[\leadsto x + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}} \]

      5. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}} \]

      6. lower-/.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\frac{t}{z \cdot 3}}}{y} \]

      7. *-commutative N/A

         \[\leadsto x + \frac{\frac{t}{\color{blue}{3 \cdot z}}}{y} \]

      8. lower-*.f64 93.0

         \[\leadsto x + \frac{\frac{t}{\color{blue}{3 \cdot z}}}{y} \]

   7. Applied rewrites 93.0%

      \[\leadsto x + \color{blue}{\frac{\frac{t}{3 \cdot z}}{y}} \]

   if 6.20000000000000018 < y < 1.5e111

   1. Initial program 99.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{1}{3} \cdot \frac{\frac{t}{y}}{z} - \frac{1}{3} \cdot \frac{y}{z} \]

      2. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{y}}{z} - \color{blue}{\frac{1}{3}} \cdot \frac{y}{z} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{y}}{z} - \frac{\frac{1}{3} \cdot y}{\color{blue}{z}} \]

      4. div-sub N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{y} - \frac{1}{3} \cdot y}{\color{blue}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{y} - \frac{1}{3} \cdot y}{\color{blue}{z}} \]

      6. distribute-lft-out-- N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \left(\frac{t}{y} - y\right)}{z} \]

      7. *-commutative N/A

         \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot \frac{1}{3}}{z} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot \frac{1}{3}}{z} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot \frac{1}{3}}{z} \]

      10. lower-/.f64 81.3

          \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot 0.3333333333333333}{z} \]

   5. Applied rewrites 81.3%

      \[\leadsto \color{blue}{\frac{\left(\frac{t}{y} - y\right) \cdot 0.3333333333333333}{z}} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot \frac{1}{3}}{\color{blue}{z}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot \frac{1}{3}}{z} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot \frac{1}{3}}{z} \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot \frac{1}{3}}{z} \]

      5. associate-/l* N/A

         \[\leadsto \left(\frac{t}{y} - y\right) \cdot \color{blue}{\frac{\frac{1}{3}}{z}} \]

      6. metadata-eval N/A

         \[\leadsto \left(\frac{t}{y} - y\right) \cdot \frac{\frac{1}{3} \cdot 1}{z} \]

      7. associate-*r/ N/A

         \[\leadsto \left(\frac{t}{y} - y\right) \cdot \left(\frac{1}{3} \cdot \color{blue}{\frac{1}{z}}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\frac{t}{y} - y\right) \cdot \color{blue}{\left(\frac{1}{3} \cdot \frac{1}{z}\right)} \]

      9. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{y} - y\right) \cdot \left(\frac{1}{3} \cdot \frac{1}{z}\right) \]

      10. lift--.f64 N/A

          \[\leadsto \left(\frac{t}{y} - y\right) \cdot \left(\color{blue}{\frac{1}{3}} \cdot \frac{1}{z}\right) \]

      11. associate-*r/ N/A

          \[\leadsto \left(\frac{t}{y} - y\right) \cdot \frac{\frac{1}{3} \cdot 1}{\color{blue}{z}} \]

      12. metadata-eval N/A

          \[\leadsto \left(\frac{t}{y} - y\right) \cdot \frac{\frac{1}{3}}{z} \]

      13. lower-/.f64 81.4

          \[\leadsto \left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{\color{blue}{z}} \]

   7. Applied rewrites 81.4%

      \[\leadsto \left(\frac{t}{y} - y\right) \cdot \color{blue}{\frac{0.3333333333333333}{z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 88.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{0.3333333333333333 \cdot y}{z}\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 14.5:\\ \;\;\;\;x + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+111}:\\ \;\;\;\;\left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ (* 0.3333333333333333 y) z))))
   (if (<= y -6.4e+15)
     t_1
     (if (<= y 14.5)
       (+ x (/ t (* z (* 3.0 y))))
       (if (<= y 1.5e+111) (* (- (/ t y) y) (/ 0.3333333333333333 z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - ((0.3333333333333333 * y) / z);
	double tmp;
	if (y <= -6.4e+15) {
		tmp = t_1;
	} else if (y <= 14.5) {
		tmp = x + (t / (z * (3.0 * y)));
	} else if (y <= 1.5e+111) {
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	} 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 - ((0.3333333333333333d0 * y) / z)
    if (y <= (-6.4d+15)) then
        tmp = t_1
    else if (y <= 14.5d0) then
        tmp = x + (t / (z * (3.0d0 * y)))
    else if (y <= 1.5d+111) then
        tmp = ((t / y) - y) * (0.3333333333333333d0 / z)
    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 - ((0.3333333333333333 * y) / z);
	double tmp;
	if (y <= -6.4e+15) {
		tmp = t_1;
	} else if (y <= 14.5) {
		tmp = x + (t / (z * (3.0 * y)));
	} else if (y <= 1.5e+111) {
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - ((0.3333333333333333 * y) / z)
	tmp = 0
	if y <= -6.4e+15:
		tmp = t_1
	elif y <= 14.5:
		tmp = x + (t / (z * (3.0 * y)))
	elif y <= 1.5e+111:
		tmp = ((t / y) - y) * (0.3333333333333333 / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(Float64(0.3333333333333333 * y) / z))
	tmp = 0.0
	if (y <= -6.4e+15)
		tmp = t_1;
	elseif (y <= 14.5)
		tmp = Float64(x + Float64(t / Float64(z * Float64(3.0 * y))));
	elseif (y <= 1.5e+111)
		tmp = Float64(Float64(Float64(t / y) - y) * Float64(0.3333333333333333 / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - ((0.3333333333333333 * y) / z);
	tmp = 0.0;
	if (y <= -6.4e+15)
		tmp = t_1;
	elseif (y <= 14.5)
		tmp = x + (t / (z * (3.0 * y)));
	elseif (y <= 1.5e+111)
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(N[(0.3333333333333333 * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.4e+15], t$95$1, If[LessEqual[y, 14.5], N[(x + N[(t / N[(z * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+111], N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.4e15 or 1.5e111 < y

   1. Initial program 98.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x - \frac{1}{3} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{\color{blue}{y}}{z} \]

      2. fp-cancel-sign-sub-inv N/A

         \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

      3. +-commutative N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \color{blue}{\frac{y}{z}}, x\right) \]

      5. lower-/.f64 95.5

         \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{\color{blue}{z}}, x\right) \]

   5. Applied rewrites 95.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \frac{y}{\color{blue}{z}}, x\right) \]

      2. lift-fma.f64 N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

      3. +-commutative N/A

         \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

      4. fp-cancel-sign-sub-inv N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{y}{z}} \]

      5. metadata-eval N/A

         \[\leadsto x - \frac{1}{3} \cdot \frac{\color{blue}{y}}{z} \]

      6. lower--.f64 N/A

         \[\leadsto x - \color{blue}{\frac{1}{3} \cdot \frac{y}{z}} \]

      7. *-commutative N/A

         \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

      8. lower-*.f64 N/A

         \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

      9. lift-/.f64 95.5

         \[\leadsto x - \frac{y}{z} \cdot 0.3333333333333333 \]

   7. Applied rewrites 95.5%

      \[\leadsto x - \color{blue}{\frac{y}{z} \cdot 0.3333333333333333} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

      2. lift-/.f64 N/A

         \[\leadsto x - \frac{y}{z} \cdot \frac{1}{3} \]

      3. *-commutative N/A

         \[\leadsto x - \frac{1}{3} \cdot \color{blue}{\frac{y}{z}} \]

      4. associate-*r/ N/A

         \[\leadsto x - \frac{\frac{1}{3} \cdot y}{\color{blue}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto x - \frac{\frac{1}{3} \cdot y}{\color{blue}{z}} \]

      6. lower-*.f64 95.7

         \[\leadsto x - \frac{0.3333333333333333 \cdot y}{z} \]

   9. Applied rewrites 95.7%

      \[\leadsto x - \frac{0.3333333333333333 \cdot y}{\color{blue}{z}} \]

   if -6.4e15 < y < 14.5

   1. Initial program 92.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 rewrites 87.4%

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

      1. lift-*.f64 N/A

         \[\leadsto x + \frac{t}{\color{blue}{\left(z \cdot 3\right)} \cdot y} \]

      2. lift-*.f64 N/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-*.f64 N/A

         \[\leadsto x + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      5. lower-*.f64 87.5

         \[\leadsto x + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]

   7. Applied rewrites 87.5%

      \[\leadsto x + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

   if 14.5 < y < 1.5e111

   1. Initial program 99.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{1}{3} \cdot \frac{\frac{t}{y}}{z} - \frac{1}{3} \cdot \frac{y}{z} \]

      2. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{y}}{z} - \color{blue}{\frac{1}{3}} \cdot \frac{y}{z} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{y}}{z} - \frac{\frac{1}{3} \cdot y}{\color{blue}{z}} \]

      4. div-sub N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{y} - \frac{1}{3} \cdot y}{\color{blue}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{y} - \frac{1}{3} \cdot y}{\color{blue}{z}} \]

      6. distribute-lft-out-- N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \left(\frac{t}{y} - y\right)}{z} \]

      7. *-commutative N/A

         \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot \frac{1}{3}}{z} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot \frac{1}{3}}{z} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot \frac{1}{3}}{z} \]

      10. lower-/.f64 80.7

          \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot 0.3333333333333333}{z} \]

   5. Applied rewrites 80.7%

      \[\leadsto \color{blue}{\frac{\left(\frac{t}{y} - y\right) \cdot 0.3333333333333333}{z}} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot \frac{1}{3}}{\color{blue}{z}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot \frac{1}{3}}{z} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot \frac{1}{3}}{z} \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot \frac{1}{3}}{z} \]

      5. associate-/l* N/A

         \[\leadsto \left(\frac{t}{y} - y\right) \cdot \color{blue}{\frac{\frac{1}{3}}{z}} \]

      6. metadata-eval N/A

         \[\leadsto \left(\frac{t}{y} - y\right) \cdot \frac{\frac{1}{3} \cdot 1}{z} \]

      7. associate-*r/ N/A

         \[\leadsto \left(\frac{t}{y} - y\right) \cdot \left(\frac{1}{3} \cdot \color{blue}{\frac{1}{z}}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\frac{t}{y} - y\right) \cdot \color{blue}{\left(\frac{1}{3} \cdot \frac{1}{z}\right)} \]

      9. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{y} - y\right) \cdot \left(\frac{1}{3} \cdot \frac{1}{z}\right) \]

      10. lift--.f64 N/A

          \[\leadsto \left(\frac{t}{y} - y\right) \cdot \left(\color{blue}{\frac{1}{3}} \cdot \frac{1}{z}\right) \]

      11. associate-*r/ N/A

          \[\leadsto \left(\frac{t}{y} - y\right) \cdot \frac{\frac{1}{3} \cdot 1}{\color{blue}{z}} \]

      12. metadata-eval N/A

          \[\leadsto \left(\frac{t}{y} - y\right) \cdot \frac{\frac{1}{3}}{z} \]

      13. lower-/.f64 80.8

          \[\leadsto \left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{\color{blue}{z}} \]

   7. Applied rewrites 80.8%

      \[\leadsto \left(\frac{t}{y} - y\right) \cdot \color{blue}{\frac{0.3333333333333333}{z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 89.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+15} \lor \neg \left(y \leq 7 \cdot 10^{+54}\right):\\ \;\;\;\;x - \frac{0.3333333333333333 \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.4e+15) (not (<= y 7e+54)))
   (- x (/ (* 0.3333333333333333 y) z))
   (+ x (/ t (* z (* 3.0 y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.4e+15) || !(y <= 7e+54)) {
		tmp = x - ((0.3333333333333333 * y) / z);
	} else {
		tmp = x + (t / (z * (3.0 * y)));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6.4d+15)) .or. (.not. (y <= 7d+54))) then
        tmp = x - ((0.3333333333333333d0 * y) / z)
    else
        tmp = x + (t / (z * (3.0d0 * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.4e+15) || !(y <= 7e+54)) {
		tmp = x - ((0.3333333333333333 * y) / z);
	} else {
		tmp = x + (t / (z * (3.0 * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.4e+15) or not (y <= 7e+54):
		tmp = x - ((0.3333333333333333 * y) / z)
	else:
		tmp = x + (t / (z * (3.0 * y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.4e+15) || !(y <= 7e+54))
		tmp = Float64(x - Float64(Float64(0.3333333333333333 * y) / z));
	else
		tmp = Float64(x + Float64(t / Float64(z * Float64(3.0 * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.4e+15) || ~((y <= 7e+54)))
		tmp = x - ((0.3333333333333333 * y) / z);
	else
		tmp = x + (t / (z * (3.0 * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.4e+15], N[Not[LessEqual[y, 7e+54]], $MachinePrecision]], N[(x - N[(N[(0.3333333333333333 * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(z * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.4e15 or 7.0000000000000002e54 < y

   1. Initial program 98.1%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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-eval N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{\color{blue}{y}}{z} \]

      2. fp-cancel-sign-sub-inv N/A

         \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

      3. +-commutative N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \color{blue}{\frac{y}{z}}, x\right) \]

      5. lower-/.f64 94.0

         \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{\color{blue}{z}}, x\right) \]

   5. Applied rewrites 94.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \frac{y}{\color{blue}{z}}, x\right) \]

      2. lift-fma.f64 N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

      3. +-commutative N/A

         \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

      4. fp-cancel-sign-sub-inv N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{y}{z}} \]

      5. metadata-eval N/A

         \[\leadsto x - \frac{1}{3} \cdot \frac{\color{blue}{y}}{z} \]

      6. lower--.f64 N/A

         \[\leadsto x - \color{blue}{\frac{1}{3} \cdot \frac{y}{z}} \]

      7. *-commutative N/A

         \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

      8. lower-*.f64 N/A

         \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

      9. lift-/.f64 94.0

         \[\leadsto x - \frac{y}{z} \cdot 0.3333333333333333 \]

   7. Applied rewrites 94.0%

      \[\leadsto x - \color{blue}{\frac{y}{z} \cdot 0.3333333333333333} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

      2. lift-/.f64 N/A

         \[\leadsto x - \frac{y}{z} \cdot \frac{1}{3} \]

      3. *-commutative N/A

         \[\leadsto x - \frac{1}{3} \cdot \color{blue}{\frac{y}{z}} \]

      4. associate-*r/ N/A

         \[\leadsto x - \frac{\frac{1}{3} \cdot y}{\color{blue}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto x - \frac{\frac{1}{3} \cdot y}{\color{blue}{z}} \]

      6. lower-*.f64 94.2

         \[\leadsto x - \frac{0.3333333333333333 \cdot y}{z} \]

   9. Applied rewrites 94.2%

      \[\leadsto x - \frac{0.3333333333333333 \cdot y}{\color{blue}{z}} \]

   if -6.4e15 < y < 7.0000000000000002e54

   1. Initial program 93.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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 rewrites 84.0%

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

      1. lift-*.f64 N/A

         \[\leadsto x + \frac{t}{\color{blue}{\left(z \cdot 3\right)} \cdot y} \]

      2. lift-*.f64 N/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-*.f64 N/A

         \[\leadsto x + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      5. lower-*.f64 84.1

         \[\leadsto x + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]

   7. Applied rewrites 84.1%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+15} \lor \neg \left(y \leq 7 \cdot 10^{+54}\right):\\ \;\;\;\;x - \frac{0.3333333333333333 \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+15} \lor \neg \left(y \leq 7 \cdot 10^{+54}\right):\\ \;\;\;\;x - \frac{0.3333333333333333 \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{z \cdot y}, 0.3333333333333333, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.4e+15) (not (<= y 7e+54)))
   (- x (/ (* 0.3333333333333333 y) z))
   (fma (/ t (* z y)) 0.3333333333333333 x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.4e+15) || !(y <= 7e+54)) {
		tmp = x - ((0.3333333333333333 * y) / z);
	} else {
		tmp = fma((t / (z * y)), 0.3333333333333333, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.4e+15) || !(y <= 7e+54))
		tmp = Float64(x - Float64(Float64(0.3333333333333333 * y) / z));
	else
		tmp = fma(Float64(t / Float64(z * y)), 0.3333333333333333, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.4e+15], N[Not[LessEqual[y, 7e+54]], $MachinePrecision]], N[(x - N[(N[(0.3333333333333333 * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision] * 0.3333333333333333 + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.4e15 or 7.0000000000000002e54 < y

   1. Initial program 98.1%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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-eval N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{\color{blue}{y}}{z} \]

      2. fp-cancel-sign-sub-inv N/A

         \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

      3. +-commutative N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \color{blue}{\frac{y}{z}}, x\right) \]

      5. lower-/.f64 94.0

         \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{\color{blue}{z}}, x\right) \]

   5. Applied rewrites 94.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \frac{y}{\color{blue}{z}}, x\right) \]

      2. lift-fma.f64 N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

      3. +-commutative N/A

         \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

      4. fp-cancel-sign-sub-inv N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{y}{z}} \]

      5. metadata-eval N/A

         \[\leadsto x - \frac{1}{3} \cdot \frac{\color{blue}{y}}{z} \]

      6. lower--.f64 N/A

         \[\leadsto x - \color{blue}{\frac{1}{3} \cdot \frac{y}{z}} \]

      7. *-commutative N/A

         \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

      8. lower-*.f64 N/A

         \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

      9. lift-/.f64 94.0

         \[\leadsto x - \frac{y}{z} \cdot 0.3333333333333333 \]

   7. Applied rewrites 94.0%

      \[\leadsto x - \color{blue}{\frac{y}{z} \cdot 0.3333333333333333} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

      2. lift-/.f64 N/A

         \[\leadsto x - \frac{y}{z} \cdot \frac{1}{3} \]

      3. *-commutative N/A

         \[\leadsto x - \frac{1}{3} \cdot \color{blue}{\frac{y}{z}} \]

      4. associate-*r/ N/A

         \[\leadsto x - \frac{\frac{1}{3} \cdot y}{\color{blue}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto x - \frac{\frac{1}{3} \cdot y}{\color{blue}{z}} \]

      6. lower-*.f64 94.2

         \[\leadsto x - \frac{0.3333333333333333 \cdot y}{z} \]

   9. Applied rewrites 94.2%

      \[\leadsto x - \frac{0.3333333333333333 \cdot y}{\color{blue}{z}} \]

   if -6.4e15 < y < 7.0000000000000002e54

   1. Initial program 93.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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-inv N/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-eval N/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-div N/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-identity N/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-inv N/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-eval N/A

          \[\leadsto x + -1 \cdot \frac{\color{blue}{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}}{z} \]

      12. +-commutative N/A

          \[\leadsto -1 \cdot \frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z} + \color{blue}{x} \]

   5. Applied rewrites 94.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{t}{y} - y}{z}, 0.3333333333333333, x\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\frac{t}{y \cdot z}, \frac{1}{3}, x\right) \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{t}{y \cdot z}, \frac{1}{3}, x\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{t}{z \cdot y}, \frac{1}{3}, x\right) \]

      3. lower-*.f64 83.9

         \[\leadsto \mathsf{fma}\left(\frac{t}{z \cdot y}, 0.3333333333333333, x\right) \]

   8. Applied rewrites 83.9%

      \[\leadsto \mathsf{fma}\left(\frac{t}{z \cdot y}, 0.3333333333333333, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+15} \lor \neg \left(y \leq 7 \cdot 10^{+54}\right):\\ \;\;\;\;x - \frac{0.3333333333333333 \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{z \cdot y}, 0.3333333333333333, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-26} \lor \neg \left(y \leq 8.1 \cdot 10^{-13}\right):\\ \;\;\;\;x - \frac{0.3333333333333333 \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z \cdot y} \cdot 0.3333333333333333\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.4e-26) (not (<= y 8.1e-13)))
   (- x (/ (* 0.3333333333333333 y) z))
   (* (/ t (* z y)) 0.3333333333333333)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.4e-26) || !(y <= 8.1e-13)) {
		tmp = x - ((0.3333333333333333 * y) / z);
	} else {
		tmp = (t / (z * y)) * 0.3333333333333333;
	}
	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 ((y <= (-2.4d-26)) .or. (.not. (y <= 8.1d-13))) then
        tmp = x - ((0.3333333333333333d0 * y) / z)
    else
        tmp = (t / (z * y)) * 0.3333333333333333d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.4e-26) || !(y <= 8.1e-13)) {
		tmp = x - ((0.3333333333333333 * y) / z);
	} else {
		tmp = (t / (z * y)) * 0.3333333333333333;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.4e-26) or not (y <= 8.1e-13):
		tmp = x - ((0.3333333333333333 * y) / z)
	else:
		tmp = (t / (z * y)) * 0.3333333333333333
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.4e-26) || !(y <= 8.1e-13))
		tmp = Float64(x - Float64(Float64(0.3333333333333333 * y) / z));
	else
		tmp = Float64(Float64(t / Float64(z * y)) * 0.3333333333333333);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.4e-26) || ~((y <= 8.1e-13)))
		tmp = x - ((0.3333333333333333 * y) / z);
	else
		tmp = (t / (z * y)) * 0.3333333333333333;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.4e-26], N[Not[LessEqual[y, 8.1e-13]], $MachinePrecision]], N[(x - N[(N[(0.3333333333333333 * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4000000000000001e-26 or 8.0999999999999998e-13 < y

   1. Initial program 98.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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-eval N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{\color{blue}{y}}{z} \]

      2. fp-cancel-sign-sub-inv N/A

         \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

      3. +-commutative N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \color{blue}{\frac{y}{z}}, x\right) \]

      5. lower-/.f64 87.0

         \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{\color{blue}{z}}, x\right) \]

   5. Applied rewrites 87.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \frac{y}{\color{blue}{z}}, x\right) \]

      2. lift-fma.f64 N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

      3. +-commutative N/A

         \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

      4. fp-cancel-sign-sub-inv N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{y}{z}} \]

      5. metadata-eval N/A

         \[\leadsto x - \frac{1}{3} \cdot \frac{\color{blue}{y}}{z} \]

      6. lower--.f64 N/A

         \[\leadsto x - \color{blue}{\frac{1}{3} \cdot \frac{y}{z}} \]

      7. *-commutative N/A

         \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

      8. lower-*.f64 N/A

         \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

      9. lift-/.f64 87.0

         \[\leadsto x - \frac{y}{z} \cdot 0.3333333333333333 \]

   7. Applied rewrites 87.0%

      \[\leadsto x - \color{blue}{\frac{y}{z} \cdot 0.3333333333333333} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

      2. lift-/.f64 N/A

         \[\leadsto x - \frac{y}{z} \cdot \frac{1}{3} \]

      3. *-commutative N/A

         \[\leadsto x - \frac{1}{3} \cdot \color{blue}{\frac{y}{z}} \]

      4. associate-*r/ N/A

         \[\leadsto x - \frac{\frac{1}{3} \cdot y}{\color{blue}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto x - \frac{\frac{1}{3} \cdot y}{\color{blue}{z}} \]

      6. lower-*.f64 87.1

         \[\leadsto x - \frac{0.3333333333333333 \cdot y}{z} \]

   9. Applied rewrites 87.1%

      \[\leadsto x - \frac{0.3333333333333333 \cdot y}{\color{blue}{z}} \]

   if -2.4000000000000001e-26 < y < 8.0999999999999998e-13

   1. Initial program 91.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{t}{y \cdot z}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{t}{y \cdot z} \cdot \frac{1}{3} \]

      4. *-commutative N/A

         \[\leadsto \frac{t}{z \cdot y} \cdot \frac{1}{3} \]

      5. lower-*.f64 66.9

         \[\leadsto \frac{t}{z \cdot y} \cdot 0.3333333333333333 \]

   5. Applied rewrites 66.9%

      \[\leadsto \color{blue}{\frac{t}{z \cdot y} \cdot 0.3333333333333333} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-26} \lor \neg \left(y \leq 8.1 \cdot 10^{-13}\right):\\ \;\;\;\;x - \frac{0.3333333333333333 \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z \cdot y} \cdot 0.3333333333333333\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.6% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.5%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
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-inv N/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-eval N/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-div N/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-identity N/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-inv N/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-eval N/A

       \[\leadsto x + -1 \cdot \frac{\color{blue}{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}}{z} \]

   12. +-commutative N/A

       \[\leadsto -1 \cdot \frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z} + \color{blue}{x} \]

5. Applied rewrites 96.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{t}{y} - y}{z}, 0.3333333333333333, x\right)} \]
6. Add Preprocessing

Alternative 8: 46.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+73} \lor \neg \left(z \leq 1.4 \cdot 10^{+158}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333 \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.8e+73) (not (<= z 1.4e+158)))
   x
   (/ (* -0.3333333333333333 y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.8e+73) || !(z <= 1.4e+158)) {
		tmp = x;
	} else {
		tmp = (-0.3333333333333333 * y) / z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.8d+73)) .or. (.not. (z <= 1.4d+158))) then
        tmp = x
    else
        tmp = ((-0.3333333333333333d0) * y) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.8e+73) || !(z <= 1.4e+158)) {
		tmp = x;
	} else {
		tmp = (-0.3333333333333333 * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.8e+73) or not (z <= 1.4e+158):
		tmp = x
	else:
		tmp = (-0.3333333333333333 * y) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.8e+73) || !(z <= 1.4e+158))
		tmp = x;
	else
		tmp = Float64(Float64(-0.3333333333333333 * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.8e+73) || ~((z <= 1.4e+158)))
		tmp = x;
	else
		tmp = (-0.3333333333333333 * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.8e+73], N[Not[LessEqual[z, 1.4e+158]], $MachinePrecision]], x, N[(N[(-0.3333333333333333 * y), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.80000000000000008e73 or 1.40000000000000001e158 < z

   1. Initial program 98.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 58.8%

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

   if -2.80000000000000008e73 < z < 1.40000000000000001e158

   1. Initial program 94.2%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{1}{3} \cdot \frac{\frac{t}{y}}{z} - \frac{1}{3} \cdot \frac{y}{z} \]

      2. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{y}}{z} - \color{blue}{\frac{1}{3}} \cdot \frac{y}{z} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{y}}{z} - \frac{\frac{1}{3} \cdot y}{\color{blue}{z}} \]

      4. div-sub N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{y} - \frac{1}{3} \cdot y}{\color{blue}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{y} - \frac{1}{3} \cdot y}{\color{blue}{z}} \]

      6. distribute-lft-out-- N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \left(\frac{t}{y} - y\right)}{z} \]

      7. *-commutative N/A

         \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot \frac{1}{3}}{z} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot \frac{1}{3}}{z} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot \frac{1}{3}}{z} \]

      10. lower-/.f64 86.4

          \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot 0.3333333333333333}{z} \]

   5. Applied rewrites 86.4%

      \[\leadsto \color{blue}{\frac{\left(\frac{t}{y} - y\right) \cdot 0.3333333333333333}{z}} \]

   6. Taylor expanded in y around inf

      \[\leadsto \frac{\frac{-1}{3} \cdot y}{z} \]
   7. Step-by-step derivation

      1. lower-*.f64 46.8

         \[\leadsto \frac{-0.3333333333333333 \cdot y}{z} \]

   8. Applied rewrites 46.8%

      \[\leadsto \frac{-0.3333333333333333 \cdot y}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+73} \lor \neg \left(z \leq 1.4 \cdot 10^{+158}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333 \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+158}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.8e+73) x (if (<= z 1.4e+158) (* -0.3333333333333333 (/ y z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+73) {
		tmp = x;
	} else if (z <= 1.4e+158) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = 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 (z <= (-2.8d+73)) then
        tmp = x
    else if (z <= 1.4d+158) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+73) {
		tmp = x;
	} else if (z <= 1.4e+158) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.8e+73:
		tmp = x
	elif z <= 1.4e+158:
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.8e+73)
		tmp = x;
	elseif (z <= 1.4e+158)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.8e+73)
		tmp = x;
	elseif (z <= 1.4e+158)
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.8e+73], x, If[LessEqual[z, 1.4e+158], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.80000000000000008e73 or 1.40000000000000001e158 < z

   1. Initial program 98.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 58.8%

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

   if -2.80000000000000008e73 < z < 1.40000000000000001e158

   1. Initial program 94.2%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   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-*.f64 N/A

         \[\leadsto \frac{-1}{3} \cdot \color{blue}{\frac{y}{z}} \]

      2. lower-/.f64 46.8

         \[\leadsto -0.3333333333333333 \cdot \frac{y}{\color{blue}{z}} \]

   5. Applied rewrites 46.8%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 63.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ x - \frac{0.3333333333333333 \cdot y}{z} \end{array} \]

FPCore

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

C

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

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 - ((0.3333333333333333d0 * y) / z)
end function

Java

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

Python

def code(x, y, z, t):
	return x - ((0.3333333333333333 * y) / z)

Julia

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

MATLAB

function tmp = code(x, y, z, t)
	tmp = x - ((0.3333333333333333 * y) / z);
end

Wolfram

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

Derivation

1. Initial program 95.5%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
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-eval N/A

      \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{\color{blue}{y}}{z} \]

   2. fp-cancel-sign-sub-inv N/A

      \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

   3. +-commutative N/A

      \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

   4. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \color{blue}{\frac{y}{z}}, x\right) \]

   5. lower-/.f64 61.8

      \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{\color{blue}{z}}, x\right) \]

5. Applied rewrites 61.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)} \]
6. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \frac{y}{\color{blue}{z}}, x\right) \]

   2. lift-fma.f64 N/A

      \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

   3. +-commutative N/A

      \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

   4. fp-cancel-sign-sub-inv N/A

      \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{y}{z}} \]

   5. metadata-eval N/A

      \[\leadsto x - \frac{1}{3} \cdot \frac{\color{blue}{y}}{z} \]

   6. lower--.f64 N/A

      \[\leadsto x - \color{blue}{\frac{1}{3} \cdot \frac{y}{z}} \]

   7. *-commutative N/A

      \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

   8. lower-*.f64 N/A

      \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

   9. lift-/.f64 61.8

      \[\leadsto x - \frac{y}{z} \cdot 0.3333333333333333 \]

7. Applied rewrites 61.8%

   \[\leadsto x - \color{blue}{\frac{y}{z} \cdot 0.3333333333333333} \]
8. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

   2. lift-/.f64 N/A

      \[\leadsto x - \frac{y}{z} \cdot \frac{1}{3} \]

   3. *-commutative N/A

      \[\leadsto x - \frac{1}{3} \cdot \color{blue}{\frac{y}{z}} \]

   4. associate-*r/ N/A

      \[\leadsto x - \frac{\frac{1}{3} \cdot y}{\color{blue}{z}} \]

   5. lower-/.f64 N/A

      \[\leadsto x - \frac{\frac{1}{3} \cdot y}{\color{blue}{z}} \]

   6. lower-*.f64 61.9

      \[\leadsto x - \frac{0.3333333333333333 \cdot y}{z} \]

9. Applied rewrites 61.9%

   \[\leadsto x - \frac{0.3333333333333333 \cdot y}{\color{blue}{z}} \]
10. Add Preprocessing

Alternative 11: 63.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ x - \frac{y}{z} \cdot 0.3333333333333333 \end{array} \]

FPCore

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

C

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

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) * 0.3333333333333333d0)
end function

Java

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

Python

def code(x, y, z, t):
	return x - ((y / z) * 0.3333333333333333)

Julia

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

MATLAB

function tmp = code(x, y, z, t)
	tmp = x - ((y / z) * 0.3333333333333333);
end

Wolfram

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

Derivation

1. Initial program 95.5%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
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-eval N/A

      \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{\color{blue}{y}}{z} \]

   2. fp-cancel-sign-sub-inv N/A

      \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

   3. +-commutative N/A

      \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

   4. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \color{blue}{\frac{y}{z}}, x\right) \]

   5. lower-/.f64 61.8

      \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{\color{blue}{z}}, x\right) \]

5. Applied rewrites 61.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)} \]
6. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \frac{y}{\color{blue}{z}}, x\right) \]

   2. lift-fma.f64 N/A

      \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

   3. +-commutative N/A

      \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

   4. fp-cancel-sign-sub-inv N/A

      \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{y}{z}} \]

   5. metadata-eval N/A

      \[\leadsto x - \frac{1}{3} \cdot \frac{\color{blue}{y}}{z} \]

   6. lower--.f64 N/A

      \[\leadsto x - \color{blue}{\frac{1}{3} \cdot \frac{y}{z}} \]

   7. *-commutative N/A

      \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

   8. lower-*.f64 N/A

      \[\leadsto x - \frac{y}{z} \cdot \color{blue}{\frac{1}{3}} \]

   9. lift-/.f64 61.8

      \[\leadsto x - \frac{y}{z} \cdot 0.3333333333333333 \]

7. Applied rewrites 61.8%

   \[\leadsto x - \color{blue}{\frac{y}{z} \cdot 0.3333333333333333} \]
8. Add Preprocessing

Alternative 12: 63.7% accurate, 2.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.5%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
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-eval N/A

      \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{\color{blue}{y}}{z} \]

   2. fp-cancel-sign-sub-inv N/A

      \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

   3. +-commutative N/A

      \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

   4. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \color{blue}{\frac{y}{z}}, x\right) \]

   5. lower-/.f64 61.8

      \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{\color{blue}{z}}, x\right) \]

5. Applied rewrites 61.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)} \]
6. Add Preprocessing

Alternative 13: 30.2% accurate, 44.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.5%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

5. Applied rewrites 26.6%

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

Developer Target 1: 96.4% accurate, 0.9× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / 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 = (x - (y / (z * 3.0d0))) + ((t / (z * 3.0d0)) / y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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]

Reproduce

herbie shell --seed 2025060 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (- x (/ y (* z 3))) (/ (/ t (* z 3)) y)))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))