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

Percentage Accurate: 79.3% → 91.4%

Time: 6.4s

Alternatives: 19

Speedup: 1.0×

• 38.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

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, a, b, c)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Initial Program: 79.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

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, a, b, c)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Alternative 1: 91.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+48}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, a \cdot t, \frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{\left(x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, \frac{y}{z}, \frac{b}{z \cdot x}\right) \cdot x\right)}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -2.9e+48)
   (/ (fma -4.0 (* a t) (/ (fma (* 9.0 y) x b) z)) c)
   (if (<= z 3.2e-6)
     (/ (+ (- (* x (* 9.0 y)) (* (* (* z 4.0) t) a)) b) (* z c))
     (/ (fma -4.0 (* a t) (* (fma 9.0 (/ y z) (/ b (* z x))) x)) c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -2.9e+48) {
		tmp = fma(-4.0, (a * t), (fma((9.0 * y), x, b) / z)) / c;
	} else if (z <= 3.2e-6) {
		tmp = (((x * (9.0 * y)) - (((z * 4.0) * t) * a)) + b) / (z * c);
	} else {
		tmp = fma(-4.0, (a * t), (fma(9.0, (y / z), (b / (z * x))) * x)) / c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -2.9e+48)
		tmp = Float64(fma(-4.0, Float64(a * t), Float64(fma(Float64(9.0 * y), x, b) / z)) / c);
	elseif (z <= 3.2e-6)
		tmp = Float64(Float64(Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c));
	else
		tmp = Float64(fma(-4.0, Float64(a * t), Float64(fma(9.0, Float64(y / z), Float64(b / Float64(z * x))) * x)) / c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -2.9e+48], N[(N[(-4.0 * N[(a * t), $MachinePrecision] + N[(N[(N[(9.0 * y), $MachinePrecision] * x + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 3.2e-6], N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(a * t), $MachinePrecision] + N[(N[(9.0 * N[(y / z), $MachinePrecision] + N[(b / N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8999999999999999e48

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   4. Applied rewrites 84.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\right)} \]

   6. Applied rewrites 86.5%

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, \frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z}\right)}{\color{blue}{c}} \]

   if -2.8999999999999999e48 < z < 3.1999999999999999e-6

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   3. Applied rewrites 79.3%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   if 3.1999999999999999e-6 < z

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   4. Applied rewrites 84.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\right)} \]

   6. Applied rewrites 86.5%

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, \frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z}\right)}{\color{blue}{c}} \]

   7. Taylor expanded in x around inf

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, x \cdot \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right)\right)}{c} \]

   9. Applied rewrites 78.0%

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, \frac{y}{z}, \frac{b}{z \cdot x}\right) \cdot x\right)}{c} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 91.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+48}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, a \cdot t, \frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 10^{-15}:\\ \;\;\;\;\frac{\left(x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, \frac{x}{z}, \frac{b}{z \cdot y}\right) \cdot y\right)}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -2.9e+48)
   (/ (fma -4.0 (* a t) (/ (fma (* 9.0 y) x b) z)) c)
   (if (<= z 1e-15)
     (/ (+ (- (* x (* 9.0 y)) (* (* (* z 4.0) t) a)) b) (* z c))
     (/ (fma -4.0 (* a t) (* (fma 9.0 (/ x z) (/ b (* z y))) y)) c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -2.9e+48) {
		tmp = fma(-4.0, (a * t), (fma((9.0 * y), x, b) / z)) / c;
	} else if (z <= 1e-15) {
		tmp = (((x * (9.0 * y)) - (((z * 4.0) * t) * a)) + b) / (z * c);
	} else {
		tmp = fma(-4.0, (a * t), (fma(9.0, (x / z), (b / (z * y))) * y)) / c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -2.9e+48)
		tmp = Float64(fma(-4.0, Float64(a * t), Float64(fma(Float64(9.0 * y), x, b) / z)) / c);
	elseif (z <= 1e-15)
		tmp = Float64(Float64(Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c));
	else
		tmp = Float64(fma(-4.0, Float64(a * t), Float64(fma(9.0, Float64(x / z), Float64(b / Float64(z * y))) * y)) / c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -2.9e+48], N[(N[(-4.0 * N[(a * t), $MachinePrecision] + N[(N[(N[(9.0 * y), $MachinePrecision] * x + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1e-15], N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(a * t), $MachinePrecision] + N[(N[(9.0 * N[(x / z), $MachinePrecision] + N[(b / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8999999999999999e48

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   4. Applied rewrites 84.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\right)} \]

   6. Applied rewrites 86.5%

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, \frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z}\right)}{\color{blue}{c}} \]

   if -2.8999999999999999e48 < z < 1.0000000000000001e-15

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   3. Applied rewrites 79.3%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   if 1.0000000000000001e-15 < z

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   4. Applied rewrites 84.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\right)} \]

   6. Applied rewrites 86.5%

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, \frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z}\right)}{\color{blue}{c}} \]

   7. Taylor expanded in y around inf

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, y \cdot \left(9 \cdot \frac{x}{z} + \frac{b}{y \cdot z}\right)\right)}{c} \]

   9. Applied rewrites 78.0%

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, \frac{x}{z}, \frac{b}{z \cdot y}\right) \cdot y\right)}{c} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 91.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(-4, a \cdot t, \frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z}\right)}{c}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-128}:\\ \;\;\;\;\frac{\left(x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma -4.0 (* a t) (/ (fma (* 9.0 y) x b) z)) c)))
   (if (<= z -2.9e+48)
     t_1
     (if (<= z 6e-128)
       (/ (+ (- (* x (* 9.0 y)) (* (* (* z 4.0) t) a)) b) (* z c))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(-4.0, (a * t), (fma((9.0 * y), x, b) / z)) / c;
	double tmp;
	if (z <= -2.9e+48) {
		tmp = t_1;
	} else if (z <= 6e-128) {
		tmp = (((x * (9.0 * y)) - (((z * 4.0) * t) * a)) + b) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(-4.0, Float64(a * t), Float64(fma(Float64(9.0 * y), x, b) / z)) / c)
	tmp = 0.0
	if (z <= -2.9e+48)
		tmp = t_1;
	elseif (z <= 6e-128)
		tmp = Float64(Float64(Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(-4.0 * N[(a * t), $MachinePrecision] + N[(N[(N[(9.0 * y), $MachinePrecision] * x + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -2.9e+48], t$95$1, If[LessEqual[z, 6e-128], N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8999999999999999e48 or 5.99999999999999956e-128 < z

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   4. Applied rewrites 84.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\right)} \]

   6. Applied rewrites 86.5%

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, \frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z}\right)}{\color{blue}{c}} \]

   if -2.8999999999999999e48 < z < 5.99999999999999956e-128

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   3. Applied rewrites 79.3%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 91.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(-4, a \cdot t, \frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z}\right)}{c}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-128}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \left(\left(t \cdot z\right) \cdot a\right) \cdot -4\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma -4.0 (* a t) (/ (fma (* 9.0 y) x b) z)) c)))
   (if (<= z -2.9e+48)
     t_1
     (if (<= z 6e-128)
       (/ (+ (fma (* x 9.0) y (* (* (* t z) a) -4.0)) b) (* z c))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(-4.0, (a * t), (fma((9.0 * y), x, b) / z)) / c;
	double tmp;
	if (z <= -2.9e+48) {
		tmp = t_1;
	} else if (z <= 6e-128) {
		tmp = (fma((x * 9.0), y, (((t * z) * a) * -4.0)) + b) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(-4.0, Float64(a * t), Float64(fma(Float64(9.0 * y), x, b) / z)) / c)
	tmp = 0.0
	if (z <= -2.9e+48)
		tmp = t_1;
	elseif (z <= 6e-128)
		tmp = Float64(Float64(fma(Float64(x * 9.0), y, Float64(Float64(Float64(t * z) * a) * -4.0)) + b) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(-4.0 * N[(a * t), $MachinePrecision] + N[(N[(N[(9.0 * y), $MachinePrecision] * x + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -2.9e+48], t$95$1, If[LessEqual[z, 6e-128], N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y + N[(N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8999999999999999e48 or 5.99999999999999956e-128 < z

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   4. Applied rewrites 84.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\right)} \]

   6. Applied rewrites 86.5%

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, \frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z}\right)}{\color{blue}{c}} \]

   if -2.8999999999999999e48 < z < 5.99999999999999956e-128

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{\left(9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)} + b}{z \cdot c} \]

   4. Applied rewrites 79.7%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x \cdot 9, y, \left(\left(t \cdot z\right) \cdot a\right) \cdot -4\right)} + b}{z \cdot c} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, a \cdot t, \frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z}\right)}{c}\\ \mathbf{elif}\;t \leq 360000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;-\frac{4 \cdot t - \frac{b}{a \cdot z}}{c} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -4.2e-6)
   (/ (fma -4.0 (* a t) (/ (fma (* 9.0 y) x b) z)) c)
   (if (<= t 360000000000.0)
     (fma (/ (* a t) c) -4.0 (/ (fma (* x 9.0) y b) (* z c)))
     (- (* (/ (- (* 4.0 t) (/ b (* a z))) c) a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -4.2e-6) {
		tmp = fma(-4.0, (a * t), (fma((9.0 * y), x, b) / z)) / c;
	} else if (t <= 360000000000.0) {
		tmp = fma(((a * t) / c), -4.0, (fma((x * 9.0), y, b) / (z * c)));
	} else {
		tmp = -((((4.0 * t) - (b / (a * z))) / c) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -4.2e-6)
		tmp = Float64(fma(-4.0, Float64(a * t), Float64(fma(Float64(9.0 * y), x, b) / z)) / c);
	elseif (t <= 360000000000.0)
		tmp = fma(Float64(Float64(a * t) / c), -4.0, Float64(fma(Float64(x * 9.0), y, b) / Float64(z * c)));
	else
		tmp = Float64(-Float64(Float64(Float64(Float64(4.0 * t) - Float64(b / Float64(a * z))) / c) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -4.2e-6], N[(N[(-4.0 * N[(a * t), $MachinePrecision] + N[(N[(N[(9.0 * y), $MachinePrecision] * x + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, 360000000000.0], N[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] * -4.0 + N[(N[(N[(x * 9.0), $MachinePrecision] * y + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-N[(N[(N[(N[(4.0 * t), $MachinePrecision] - N[(b / N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] * a), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if t < -4.1999999999999996e-6

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   4. Applied rewrites 84.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\right)} \]

   6. Applied rewrites 86.5%

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, \frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z}\right)}{\color{blue}{c}} \]

   if -4.1999999999999996e-6 < t < 3.6e11

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   4. Applied rewrites 84.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\right)} \]

   if 3.6e11 < t

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \frac{9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}}{a} + 4 \cdot \frac{t}{c}\right)\right)} \]

   4. Applied rewrites 78.3%

      \[\leadsto \color{blue}{-\mathsf{fma}\left(4, \frac{t}{c}, -\frac{\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}}{a}\right) \cdot a} \]

   5. Taylor expanded in x around 0

      \[\leadsto -\left(4 \cdot \frac{t}{c} - \frac{b}{a \cdot \left(c \cdot z\right)}\right) \cdot a \]

   7. Applied rewrites 60.0%

      \[\leadsto -\left(\frac{4 \cdot t}{c} - \frac{b}{\left(z \cdot c\right) \cdot a}\right) \cdot a \]

   8. Taylor expanded in c around 0

      \[\leadsto -\frac{4 \cdot t - \frac{b}{a \cdot z}}{c} \cdot a \]

   10. Applied rewrites 61.3%

       \[\leadsto -\frac{4 \cdot t - \frac{b}{a \cdot z}}{c} \cdot a \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 83.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq 1.9 \cdot 10^{+233}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, a \cdot t, \frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot \frac{t}{c}, -4, \frac{b}{z \cdot c}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 1.9e+233)
   (/ (fma -4.0 (* a t) (/ (fma (* 9.0 y) x b) z)) c)
   (fma (* a (/ t c)) -4.0 (/ b (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 1.9e+233) {
		tmp = fma(-4.0, (a * t), (fma((9.0 * y), x, b) / z)) / c;
	} else {
		tmp = fma((a * (t / c)), -4.0, (b / (z * c)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 1.9e+233)
		tmp = Float64(fma(-4.0, Float64(a * t), Float64(fma(Float64(9.0 * y), x, b) / z)) / c);
	else
		tmp = fma(Float64(a * Float64(t / c)), -4.0, Float64(b / Float64(z * c)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 1.9e+233], N[(N[(-4.0 * N[(a * t), $MachinePrecision] + N[(N[(N[(9.0 * y), $MachinePrecision] * x + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 1.8999999999999999e233

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   4. Applied rewrites 84.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\right)} \]

   6. Applied rewrites 86.5%

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, \frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z}\right)}{\color{blue}{c}} \]

   if 1.8999999999999999e233 < c

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   4. Applied rewrites 84.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{b}{z \cdot c}\right) \]

   7. Applied rewrites 62.7%

      \[\leadsto \mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{b}{z \cdot c}\right) \]

   9. Applied rewrites 62.7%

      \[\leadsto \mathsf{fma}\left(a \cdot \frac{t}{c}, -4, \frac{b}{z \cdot c}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 75.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{\mathsf{fma}\left(-4, a \cdot t, \frac{9 \cdot y}{z} \cdot x\right)}{c}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-102}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+37}:\\ \;\;\;\;-\frac{4 \cdot t - \frac{b}{a \cdot z}}{c} \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y))
        (t_2 (/ (fma -4.0 (* a t) (* (/ (* 9.0 y) z) x)) c)))
   (if (<= t_1 -1e-102)
     t_2
     (if (<= t_1 5e+37) (- (* (/ (- (* 4.0 t) (/ b (* a z))) c) a)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = fma(-4.0, (a * t), (((9.0 * y) / z) * x)) / c;
	double tmp;
	if (t_1 <= -1e-102) {
		tmp = t_2;
	} else if (t_1 <= 5e+37) {
		tmp = -((((4.0 * t) - (b / (a * z))) / c) * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(fma(-4.0, Float64(a * t), Float64(Float64(Float64(9.0 * y) / z) * x)) / c)
	tmp = 0.0
	if (t_1 <= -1e-102)
		tmp = t_2;
	elseif (t_1 <= 5e+37)
		tmp = Float64(-Float64(Float64(Float64(Float64(4.0 * t) - Float64(b / Float64(a * z))) / c) * a));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(-4.0 * N[(a * t), $MachinePrecision] + N[(N[(N[(9.0 * y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-102], t$95$2, If[LessEqual[t$95$1, 5e+37], (-N[(N[(N[(N[(4.0 * t), $MachinePrecision] - N[(b / N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] * a), $MachinePrecision]), t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999933e-103 or 4.99999999999999989e37 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   4. Applied rewrites 84.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\right)} \]

   6. Applied rewrites 86.5%

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, \frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z}\right)}{\color{blue}{c}} \]

   7. Taylor expanded in x around inf

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, x \cdot \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right)\right)}{c} \]

   9. Applied rewrites 78.0%

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, \frac{y}{z}, \frac{b}{z \cdot x}\right) \cdot x\right)}{c} \]

   10. Taylor expanded in x around inf

       \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, \left(9 \cdot \frac{y}{z}\right) \cdot x\right)}{c} \]

   12. Applied rewrites 64.9%

       \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, \frac{9 \cdot y}{z} \cdot x\right)}{c} \]

   if -9.99999999999999933e-103 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999989e37

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \frac{9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}}{a} + 4 \cdot \frac{t}{c}\right)\right)} \]

   4. Applied rewrites 78.3%

      \[\leadsto \color{blue}{-\mathsf{fma}\left(4, \frac{t}{c}, -\frac{\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}}{a}\right) \cdot a} \]

   5. Taylor expanded in x around 0

      \[\leadsto -\left(4 \cdot \frac{t}{c} - \frac{b}{a \cdot \left(c \cdot z\right)}\right) \cdot a \]

   7. Applied rewrites 60.0%

      \[\leadsto -\left(\frac{4 \cdot t}{c} - \frac{b}{\left(z \cdot c\right) \cdot a}\right) \cdot a \]

   8. Taylor expanded in c around 0

      \[\leadsto -\frac{4 \cdot t - \frac{b}{a \cdot z}}{c} \cdot a \]

   10. Applied rewrites 61.3%

       \[\leadsto -\frac{4 \cdot t - \frac{b}{a \cdot z}}{c} \cdot a \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 75.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 9, -4 \cdot \left(a \cdot t\right)\right)}{c}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-102}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+37}:\\ \;\;\;\;-\frac{4 \cdot t - \frac{b}{a \cdot z}}{c} \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y))
        (t_2 (/ (fma (/ (* y x) z) 9.0 (* -4.0 (* a t))) c)))
   (if (<= t_1 -1e-102)
     t_2
     (if (<= t_1 5e+37) (- (* (/ (- (* 4.0 t) (/ b (* a z))) c) a)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = fma(((y * x) / z), 9.0, (-4.0 * (a * t))) / c;
	double tmp;
	if (t_1 <= -1e-102) {
		tmp = t_2;
	} else if (t_1 <= 5e+37) {
		tmp = -((((4.0 * t) - (b / (a * z))) / c) * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(fma(Float64(Float64(y * x) / z), 9.0, Float64(-4.0 * Float64(a * t))) / c)
	tmp = 0.0
	if (t_1 <= -1e-102)
		tmp = t_2;
	elseif (t_1 <= 5e+37)
		tmp = Float64(-Float64(Float64(Float64(Float64(4.0 * t) - Float64(b / Float64(a * z))) / c) * a));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] * 9.0 + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-102], t$95$2, If[LessEqual[t$95$1, 5e+37], (-N[(N[(N[(N[(4.0 * t), $MachinePrecision] - N[(b / N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] * a), $MachinePrecision]), t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999933e-103 or 4.99999999999999989e37 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   4. Applied rewrites 84.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\right)} \]

   6. Applied rewrites 86.5%

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, \frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z}\right)}{\color{blue}{c}} \]

   7. Taylor expanded in b around 0

      \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c} \]

   9. Applied rewrites 63.7%

      \[\leadsto \frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 9, -4 \cdot \left(a \cdot t\right)\right)}{c} \]

   if -9.99999999999999933e-103 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999989e37

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \frac{9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}}{a} + 4 \cdot \frac{t}{c}\right)\right)} \]

   4. Applied rewrites 78.3%

      \[\leadsto \color{blue}{-\mathsf{fma}\left(4, \frac{t}{c}, -\frac{\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}}{a}\right) \cdot a} \]

   5. Taylor expanded in x around 0

      \[\leadsto -\left(4 \cdot \frac{t}{c} - \frac{b}{a \cdot \left(c \cdot z\right)}\right) \cdot a \]

   7. Applied rewrites 60.0%

      \[\leadsto -\left(\frac{4 \cdot t}{c} - \frac{b}{\left(z \cdot c\right) \cdot a}\right) \cdot a \]

   8. Taylor expanded in c around 0

      \[\leadsto -\frac{4 \cdot t - \frac{b}{a \cdot z}}{c} \cdot a \]

   10. Applied rewrites 61.3%

       \[\leadsto -\frac{4 \cdot t - \frac{b}{a \cdot z}}{c} \cdot a \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 74.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{b}{z \cdot c}\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+25}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, a \cdot t, \frac{b}{z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -2.05e+27)
   (fma (/ (* a t) c) -4.0 (/ b (* z c)))
   (if (<= z 5.8e+25)
     (/ (fma (* 9.0 y) x b) (* z c))
     (/ (fma -4.0 (* a t) (/ b z)) c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -2.05e+27) {
		tmp = fma(((a * t) / c), -4.0, (b / (z * c)));
	} else if (z <= 5.8e+25) {
		tmp = fma((9.0 * y), x, b) / (z * c);
	} else {
		tmp = fma(-4.0, (a * t), (b / z)) / c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -2.05e+27)
		tmp = fma(Float64(Float64(a * t) / c), -4.0, Float64(b / Float64(z * c)));
	elseif (z <= 5.8e+25)
		tmp = Float64(fma(Float64(9.0 * y), x, b) / Float64(z * c));
	else
		tmp = Float64(fma(-4.0, Float64(a * t), Float64(b / z)) / c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -2.05e+27], N[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] * -4.0 + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+25], N[(N[(N[(9.0 * y), $MachinePrecision] * x + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(a * t), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0500000000000001e27

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   4. Applied rewrites 84.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{b}{z \cdot c}\right) \]

   7. Applied rewrites 62.7%

      \[\leadsto \mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{b}{z \cdot c}\right) \]

   if -2.0500000000000001e27 < z < 5.7999999999999998e25

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   4. Applied rewrites 84.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

   7. Applied rewrites 59.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z \cdot c}} \]

   if 5.7999999999999998e25 < z

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   4. Applied rewrites 84.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\right)} \]

   6. Applied rewrites 86.5%

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, \frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z}\right)}{\color{blue}{c}} \]

   7. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, \frac{b}{z}\right)}{c} \]

   9. Applied rewrites 64.2%

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, \frac{b}{z}\right)}{c} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 73.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(-4, a \cdot t, \frac{b}{z}\right)}{c}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+25}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma -4.0 (* a t) (/ b z)) c)))
   (if (<= z -2.05e+27)
     t_1
     (if (<= z 5.8e+25) (/ (fma (* 9.0 y) x b) (* z c)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(-4.0, (a * t), (b / z)) / c;
	double tmp;
	if (z <= -2.05e+27) {
		tmp = t_1;
	} else if (z <= 5.8e+25) {
		tmp = fma((9.0 * y), x, b) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(-4.0, Float64(a * t), Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -2.05e+27)
		tmp = t_1;
	elseif (z <= 5.8e+25)
		tmp = Float64(fma(Float64(9.0 * y), x, b) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(-4.0 * N[(a * t), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -2.05e+27], t$95$1, If[LessEqual[z, 5.8e+25], N[(N[(N[(9.0 * y), $MachinePrecision] * x + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0500000000000001e27 or 5.7999999999999998e25 < z

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   4. Applied rewrites 84.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\right)} \]

   6. Applied rewrites 86.5%

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, \frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z}\right)}{\color{blue}{c}} \]

   7. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, \frac{b}{z}\right)}{c} \]

   9. Applied rewrites 64.2%

      \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot t, \frac{b}{z}\right)}{c} \]

   if -2.0500000000000001e27 < z < 5.7999999999999998e25

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   4. Applied rewrites 84.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

   7. Applied rewrites 59.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z \cdot c}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 68.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(a \cdot t\right) \cdot -4}{c}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+140}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* (* a t) -4.0) c)))
   (if (<= z -1.1e+145)
     t_1
     (if (<= z 2.35e+140) (/ (fma (* 9.0 y) x b) (* z c)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((a * t) * -4.0) / c;
	double tmp;
	if (z <= -1.1e+145) {
		tmp = t_1;
	} else if (z <= 2.35e+140) {
		tmp = fma((9.0 * y), x, b) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(a * t) * -4.0) / c)
	tmp = 0.0
	if (z <= -1.1e+145)
		tmp = t_1;
	elseif (z <= 2.35e+140)
		tmp = Float64(fma(Float64(9.0 * y), x, b) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.1e+145], t$95$1, If[LessEqual[z, 2.35e+140], N[(N[(N[(9.0 * y), $MachinePrecision] * x + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.10000000000000004e145 or 2.35000000000000015e140 < z

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

   4. Applied rewrites 38.7%

      \[\leadsto \color{blue}{\frac{\left(a \cdot t\right) \cdot -4}{c}} \]

   if -1.10000000000000004e145 < z < 2.35000000000000015e140

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   4. Applied rewrites 84.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, \frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

   7. Applied rewrites 59.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(9 \cdot y, x, b\right)}{z \cdot c}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 52.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;\frac{y \cdot x}{z \cdot c} \cdot 9\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+85}:\\ \;\;\;\;-\frac{4 \cdot t}{c} \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y \cdot x}{z} \cdot 9}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -4e+146)
     (* (/ (* y x) (* z c)) 9.0)
     (if (<= t_1 5e+85)
       (- (* (/ (* 4.0 t) c) a))
       (/ (* (/ (* y x) z) 9.0) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -4e+146) {
		tmp = ((y * x) / (z * c)) * 9.0;
	} else if (t_1 <= 5e+85) {
		tmp = -(((4.0 * t) / c) * a);
	} else {
		tmp = (((y * x) / z) * 9.0) / c;
	}
	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, a, b, c)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 9.0d0) * y
    if (t_1 <= (-4d+146)) then
        tmp = ((y * x) / (z * c)) * 9.0d0
    else if (t_1 <= 5d+85) then
        tmp = -(((4.0d0 * t) / c) * a)
    else
        tmp = (((y * x) / z) * 9.0d0) / c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -4e+146) {
		tmp = ((y * x) / (z * c)) * 9.0;
	} else if (t_1 <= 5e+85) {
		tmp = -(((4.0 * t) / c) * a);
	} else {
		tmp = (((y * x) / z) * 9.0) / c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	tmp = 0
	if t_1 <= -4e+146:
		tmp = ((y * x) / (z * c)) * 9.0
	elif t_1 <= 5e+85:
		tmp = -(((4.0 * t) / c) * a)
	else:
		tmp = (((y * x) / z) * 9.0) / c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -4e+146)
		tmp = Float64(Float64(Float64(y * x) / Float64(z * c)) * 9.0);
	elseif (t_1 <= 5e+85)
		tmp = Float64(-Float64(Float64(Float64(4.0 * t) / c) * a));
	else
		tmp = Float64(Float64(Float64(Float64(y * x) / z) * 9.0) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	tmp = 0.0;
	if (t_1 <= -4e+146)
		tmp = ((y * x) / (z * c)) * 9.0;
	elseif (t_1 <= 5e+85)
		tmp = -(((4.0 * t) / c) * a);
	else
		tmp = (((y * x) / z) * 9.0) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+146], N[(N[(N[(y * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+85], (-N[(N[(N[(4.0 * t), $MachinePrecision] / c), $MachinePrecision] * a), $MachinePrecision]), N[(N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] * 9.0), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.99999999999999973e146

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]

   4. Applied rewrites 35.7%

      \[\leadsto \color{blue}{\frac{\left(y \cdot x\right) \cdot 9}{z \cdot c}} \]

   6. Applied rewrites 35.7%

      \[\leadsto \frac{y \cdot x}{z \cdot c} \cdot \color{blue}{9} \]

   if -3.99999999999999973e146 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.0000000000000001e85

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \frac{9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}}{a} + 4 \cdot \frac{t}{c}\right)\right)} \]

   4. Applied rewrites 78.3%

      \[\leadsto \color{blue}{-\mathsf{fma}\left(4, \frac{t}{c}, -\frac{\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}}{a}\right) \cdot a} \]

   5. Taylor expanded in z around inf

      \[\leadsto -\left(4 \cdot \frac{t}{c}\right) \cdot a \]

   7. Applied rewrites 40.2%

      \[\leadsto -\frac{4 \cdot t}{c} \cdot a \]

   if 5.0000000000000001e85 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]

   4. Applied rewrites 35.7%

      \[\leadsto \color{blue}{\frac{\left(y \cdot x\right) \cdot 9}{z \cdot c}} \]

   6. Applied rewrites 34.4%

      \[\leadsto \frac{\frac{\left(y \cdot x\right) \cdot 9}{z}}{\color{blue}{c}} \]

   8. Applied rewrites 34.4%

      \[\leadsto \frac{\frac{y \cdot x}{z} \cdot 9}{c} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 52.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;\frac{y \cdot x}{z \cdot c} \cdot 9\\ \mathbf{elif}\;t\_1 \leq 10^{+134}:\\ \;\;\;\;-\frac{4 \cdot t}{c} \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(9 \cdot y\right) \cdot x}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -4e+146)
     (* (/ (* y x) (* z c)) 9.0)
     (if (<= t_1 1e+134)
       (- (* (/ (* 4.0 t) c) a))
       (/ (* (* 9.0 y) x) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -4e+146) {
		tmp = ((y * x) / (z * c)) * 9.0;
	} else if (t_1 <= 1e+134) {
		tmp = -(((4.0 * t) / c) * a);
	} else {
		tmp = ((9.0 * y) * x) / (z * c);
	}
	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, a, b, c)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 9.0d0) * y
    if (t_1 <= (-4d+146)) then
        tmp = ((y * x) / (z * c)) * 9.0d0
    else if (t_1 <= 1d+134) then
        tmp = -(((4.0d0 * t) / c) * a)
    else
        tmp = ((9.0d0 * y) * x) / (z * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -4e+146) {
		tmp = ((y * x) / (z * c)) * 9.0;
	} else if (t_1 <= 1e+134) {
		tmp = -(((4.0 * t) / c) * a);
	} else {
		tmp = ((9.0 * y) * x) / (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	tmp = 0
	if t_1 <= -4e+146:
		tmp = ((y * x) / (z * c)) * 9.0
	elif t_1 <= 1e+134:
		tmp = -(((4.0 * t) / c) * a)
	else:
		tmp = ((9.0 * y) * x) / (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -4e+146)
		tmp = Float64(Float64(Float64(y * x) / Float64(z * c)) * 9.0);
	elseif (t_1 <= 1e+134)
		tmp = Float64(-Float64(Float64(Float64(4.0 * t) / c) * a));
	else
		tmp = Float64(Float64(Float64(9.0 * y) * x) / Float64(z * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	tmp = 0.0;
	if (t_1 <= -4e+146)
		tmp = ((y * x) / (z * c)) * 9.0;
	elseif (t_1 <= 1e+134)
		tmp = -(((4.0 * t) / c) * a);
	else
		tmp = ((9.0 * y) * x) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+146], N[(N[(N[(y * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+134], (-N[(N[(N[(4.0 * t), $MachinePrecision] / c), $MachinePrecision] * a), $MachinePrecision]), N[(N[(N[(9.0 * y), $MachinePrecision] * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.99999999999999973e146

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]

   4. Applied rewrites 35.7%

      \[\leadsto \color{blue}{\frac{\left(y \cdot x\right) \cdot 9}{z \cdot c}} \]

   6. Applied rewrites 35.7%

      \[\leadsto \frac{y \cdot x}{z \cdot c} \cdot \color{blue}{9} \]

   if -3.99999999999999973e146 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.99999999999999921e133

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \frac{9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}}{a} + 4 \cdot \frac{t}{c}\right)\right)} \]

   4. Applied rewrites 78.3%

      \[\leadsto \color{blue}{-\mathsf{fma}\left(4, \frac{t}{c}, -\frac{\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}}{a}\right) \cdot a} \]

   5. Taylor expanded in z around inf

      \[\leadsto -\left(4 \cdot \frac{t}{c}\right) \cdot a \]

   7. Applied rewrites 40.2%

      \[\leadsto -\frac{4 \cdot t}{c} \cdot a \]

   if 9.99999999999999921e133 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]

   4. Applied rewrites 35.7%

      \[\leadsto \color{blue}{\frac{\left(y \cdot x\right) \cdot 9}{z \cdot c}} \]

   6. Applied rewrites 35.7%

      \[\leadsto \frac{\left(9 \cdot y\right) \cdot x}{\color{blue}{z} \cdot c} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 52.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;\frac{y \cdot x}{z \cdot c} \cdot 9\\ \mathbf{elif}\;t\_1 \leq 10^{+134}:\\ \;\;\;\;-\frac{4 \cdot t}{c} \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(9 \cdot x\right) \cdot y}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -4e+146)
     (* (/ (* y x) (* z c)) 9.0)
     (if (<= t_1 1e+134)
       (- (* (/ (* 4.0 t) c) a))
       (/ (* (* 9.0 x) y) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -4e+146) {
		tmp = ((y * x) / (z * c)) * 9.0;
	} else if (t_1 <= 1e+134) {
		tmp = -(((4.0 * t) / c) * a);
	} else {
		tmp = ((9.0 * x) * y) / (z * c);
	}
	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, a, b, c)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 9.0d0) * y
    if (t_1 <= (-4d+146)) then
        tmp = ((y * x) / (z * c)) * 9.0d0
    else if (t_1 <= 1d+134) then
        tmp = -(((4.0d0 * t) / c) * a)
    else
        tmp = ((9.0d0 * x) * y) / (z * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -4e+146) {
		tmp = ((y * x) / (z * c)) * 9.0;
	} else if (t_1 <= 1e+134) {
		tmp = -(((4.0 * t) / c) * a);
	} else {
		tmp = ((9.0 * x) * y) / (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	tmp = 0
	if t_1 <= -4e+146:
		tmp = ((y * x) / (z * c)) * 9.0
	elif t_1 <= 1e+134:
		tmp = -(((4.0 * t) / c) * a)
	else:
		tmp = ((9.0 * x) * y) / (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -4e+146)
		tmp = Float64(Float64(Float64(y * x) / Float64(z * c)) * 9.0);
	elseif (t_1 <= 1e+134)
		tmp = Float64(-Float64(Float64(Float64(4.0 * t) / c) * a));
	else
		tmp = Float64(Float64(Float64(9.0 * x) * y) / Float64(z * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	tmp = 0.0;
	if (t_1 <= -4e+146)
		tmp = ((y * x) / (z * c)) * 9.0;
	elseif (t_1 <= 1e+134)
		tmp = -(((4.0 * t) / c) * a);
	else
		tmp = ((9.0 * x) * y) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+146], N[(N[(N[(y * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+134], (-N[(N[(N[(4.0 * t), $MachinePrecision] / c), $MachinePrecision] * a), $MachinePrecision]), N[(N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.99999999999999973e146

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]

   4. Applied rewrites 35.7%

      \[\leadsto \color{blue}{\frac{\left(y \cdot x\right) \cdot 9}{z \cdot c}} \]

   6. Applied rewrites 35.7%

      \[\leadsto \frac{y \cdot x}{z \cdot c} \cdot \color{blue}{9} \]

   if -3.99999999999999973e146 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.99999999999999921e133

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \frac{9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}}{a} + 4 \cdot \frac{t}{c}\right)\right)} \]

   4. Applied rewrites 78.3%

      \[\leadsto \color{blue}{-\mathsf{fma}\left(4, \frac{t}{c}, -\frac{\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}}{a}\right) \cdot a} \]

   5. Taylor expanded in z around inf

      \[\leadsto -\left(4 \cdot \frac{t}{c}\right) \cdot a \]

   7. Applied rewrites 40.2%

      \[\leadsto -\frac{4 \cdot t}{c} \cdot a \]

   if 9.99999999999999921e133 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]

   4. Applied rewrites 35.7%

      \[\leadsto \color{blue}{\frac{\left(y \cdot x\right) \cdot 9}{z \cdot c}} \]

   6. Applied rewrites 35.7%

      \[\leadsto \frac{\left(9 \cdot x\right) \cdot y}{\color{blue}{z} \cdot c} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 52.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{y \cdot x}{z \cdot c} \cdot 9\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+146}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+134}:\\ \;\;\;\;-\frac{4 \cdot t}{c} \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (* (/ (* y x) (* z c)) 9.0)))
   (if (<= t_1 -4e+146)
     t_2
     (if (<= t_1 1e+134) (- (* (/ (* 4.0 t) c) a)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = ((y * x) / (z * c)) * 9.0;
	double tmp;
	if (t_1 <= -4e+146) {
		tmp = t_2;
	} else if (t_1 <= 1e+134) {
		tmp = -(((4.0 * t) / c) * a);
	} else {
		tmp = t_2;
	}
	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, a, b, c)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * 9.0d0) * y
    t_2 = ((y * x) / (z * c)) * 9.0d0
    if (t_1 <= (-4d+146)) then
        tmp = t_2
    else if (t_1 <= 1d+134) then
        tmp = -(((4.0d0 * t) / c) * a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = ((y * x) / (z * c)) * 9.0;
	double tmp;
	if (t_1 <= -4e+146) {
		tmp = t_2;
	} else if (t_1 <= 1e+134) {
		tmp = -(((4.0 * t) / c) * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	t_2 = ((y * x) / (z * c)) * 9.0
	tmp = 0
	if t_1 <= -4e+146:
		tmp = t_2
	elif t_1 <= 1e+134:
		tmp = -(((4.0 * t) / c) * a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(Float64(Float64(y * x) / Float64(z * c)) * 9.0)
	tmp = 0.0
	if (t_1 <= -4e+146)
		tmp = t_2;
	elseif (t_1 <= 1e+134)
		tmp = Float64(-Float64(Float64(Float64(4.0 * t) / c) * a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	t_2 = ((y * x) / (z * c)) * 9.0;
	tmp = 0.0;
	if (t_1 <= -4e+146)
		tmp = t_2;
	elseif (t_1 <= 1e+134)
		tmp = -(((4.0 * t) / c) * a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+146], t$95$2, If[LessEqual[t$95$1, 1e+134], (-N[(N[(N[(4.0 * t), $MachinePrecision] / c), $MachinePrecision] * a), $MachinePrecision]), t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -3.99999999999999973e146 or 9.99999999999999921e133 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]

   4. Applied rewrites 35.7%

      \[\leadsto \color{blue}{\frac{\left(y \cdot x\right) \cdot 9}{z \cdot c}} \]

   6. Applied rewrites 35.7%

      \[\leadsto \frac{y \cdot x}{z \cdot c} \cdot \color{blue}{9} \]

   if -3.99999999999999973e146 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.99999999999999921e133

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \frac{9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}}{a} + 4 \cdot \frac{t}{c}\right)\right)} \]

   4. Applied rewrites 78.3%

      \[\leadsto \color{blue}{-\mathsf{fma}\left(4, \frac{t}{c}, -\frac{\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}}{a}\right) \cdot a} \]

   5. Taylor expanded in z around inf

      \[\leadsto -\left(4 \cdot \frac{t}{c}\right) \cdot a \]

   7. Applied rewrites 40.2%

      \[\leadsto -\frac{4 \cdot t}{c} \cdot a \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 49.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+104}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 7.1 \cdot 10^{+131}:\\ \;\;\;\;-\frac{4 \cdot t}{c} \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -5.5e+104)
   (/ (/ b c) z)
   (if (<= b 7.1e+131) (- (* (/ (* 4.0 t) c) a)) (/ b (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -5.5e+104) {
		tmp = (b / c) / z;
	} else if (b <= 7.1e+131) {
		tmp = -(((4.0 * t) / c) * a);
	} else {
		tmp = b / (z * c);
	}
	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, a, b, c)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-5.5d+104)) then
        tmp = (b / c) / z
    else if (b <= 7.1d+131) then
        tmp = -(((4.0d0 * t) / c) * a)
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -5.5e+104) {
		tmp = (b / c) / z;
	} else if (b <= 7.1e+131) {
		tmp = -(((4.0 * t) / c) * a);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -5.5e+104:
		tmp = (b / c) / z
	elif b <= 7.1e+131:
		tmp = -(((4.0 * t) / c) * a)
	else:
		tmp = b / (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -5.5e+104)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= 7.1e+131)
		tmp = Float64(-Float64(Float64(Float64(4.0 * t) / c) * a));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -5.5e+104)
		tmp = (b / c) / z;
	elseif (b <= 7.1e+131)
		tmp = -(((4.0 * t) / c) * a);
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -5.5e+104], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 7.1e+131], (-N[(N[(N[(4.0 * t), $MachinePrecision] / c), $MachinePrecision] * a), $MachinePrecision]), N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.50000000000000017e104

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   4. Applied rewrites 35.0%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   6. Applied rewrites 34.6%

      \[\leadsto \frac{\frac{b}{c}}{\color{blue}{z}} \]

   if -5.50000000000000017e104 < b < 7.09999999999999941e131

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \frac{9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}}{a} + 4 \cdot \frac{t}{c}\right)\right)} \]

   4. Applied rewrites 78.3%

      \[\leadsto \color{blue}{-\mathsf{fma}\left(4, \frac{t}{c}, -\frac{\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z \cdot c}}{a}\right) \cdot a} \]

   5. Taylor expanded in z around inf

      \[\leadsto -\left(4 \cdot \frac{t}{c}\right) \cdot a \]

   7. Applied rewrites 40.2%

      \[\leadsto -\frac{4 \cdot t}{c} \cdot a \]

   if 7.09999999999999941e131 < b

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   4. Applied rewrites 35.0%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 48.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(a \cdot t\right) \cdot -4}{c}\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-157}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* (* a t) -4.0) c)))
   (if (<= z -3.9e+27) t_1 (if (<= z 1.06e-157) (/ b (* z c)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((a * t) * -4.0) / c;
	double tmp;
	if (z <= -3.9e+27) {
		tmp = t_1;
	} else if (z <= 1.06e-157) {
		tmp = b / (z * c);
	} 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, a, b, c)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((a * t) * (-4.0d0)) / c
    if (z <= (-3.9d+27)) then
        tmp = t_1
    else if (z <= 1.06d-157) then
        tmp = b / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((a * t) * -4.0) / c;
	double tmp;
	if (z <= -3.9e+27) {
		tmp = t_1;
	} else if (z <= 1.06e-157) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((a * t) * -4.0) / c
	tmp = 0
	if z <= -3.9e+27:
		tmp = t_1
	elif z <= 1.06e-157:
		tmp = b / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(a * t) * -4.0) / c)
	tmp = 0.0
	if (z <= -3.9e+27)
		tmp = t_1;
	elseif (z <= 1.06e-157)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((a * t) * -4.0) / c;
	tmp = 0.0;
	if (z <= -3.9e+27)
		tmp = t_1;
	elseif (z <= 1.06e-157)
		tmp = b / (z * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -3.9e+27], t$95$1, If[LessEqual[z, 1.06e-157], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8999999999999999e27 or 1.06e-157 < z

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

   4. Applied rewrites 38.7%

      \[\leadsto \color{blue}{\frac{\left(a \cdot t\right) \cdot -4}{c}} \]

   if -3.8999999999999999e27 < z < 1.06e-157

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   4. Applied rewrites 35.0%

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

Alternative 18: 35.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -4e+37) (/ (/ b c) z) (/ b (* z c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -4e+37) {
		tmp = (b / c) / z;
	} else {
		tmp = b / (z * c);
	}
	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, a, b, c)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-4d+37)) then
        tmp = (b / c) / z
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -4e+37) {
		tmp = (b / c) / z;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -4e+37:
		tmp = (b / c) / z
	else:
		tmp = b / (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -4e+37)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -4e+37)
		tmp = (b / c) / z;
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -4e+37], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.99999999999999982e37

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   4. Applied rewrites 35.0%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   6. Applied rewrites 34.6%

      \[\leadsto \frac{\frac{b}{c}}{\color{blue}{z}} \]

   if -3.99999999999999982e37 < b

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   4. Applied rewrites 35.0%

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

Alternative 19: 35.0% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

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, a, b, c)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return b / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.3%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

2. Taylor expanded in b around inf

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

4. Applied rewrites 35.0%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025141 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64
  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))