Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B

Percentage Accurate: 76.1% → 87.2%

Time: 8.4s

Alternatives: 11

Speedup: 0.2×

Specification

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

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)
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
    code = (x + ((y * z) / t)) / ((a + 1.0d0) + ((y * b) / t))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Python

def code(x, y, z, t, a, b):
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 76.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

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)
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
    code = (x + ((y * z) / t)) / ((a + 1.0d0) + ((y * b) / t))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Python

def code(x, y, z, t, a, b):
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 87.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-303}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{y}{t}, b, a\right), t, t\right)}, y, \frac{x}{\mathsf{fma}\left(\frac{y}{t}, b, a - -1\right)}\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(t, x, y \cdot z\right)}{b}}{y}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{\mathsf{fma}\left(\mathsf{fma}\left(b, y, t\right), \frac{1}{t}, a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{x}{y}, t, z\right)}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 -5e-303)
     (fma (/ z (fma (fma (/ y t) b a) t t)) y (/ x (fma (/ y t) b (- a -1.0))))
     (if (<= t_1 0.0)
       (/ (/ (fma t x (* y z)) b) y)
       (if (<= t_1 INFINITY)
         (/ (fma (/ y t) z x) (fma (fma b y t) (/ 1.0 t) a))
         (/ (fma (/ x y) t z) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -5e-303) {
		tmp = fma((z / fma(fma((y / t), b, a), t, t)), y, (x / fma((y / t), b, (a - -1.0))));
	} else if (t_1 <= 0.0) {
		tmp = (fma(t, x, (y * z)) / b) / y;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = fma((y / t), z, x) / fma(fma(b, y, t), (1.0 / t), a);
	} else {
		tmp = fma((x / y), t, z) / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= -5e-303)
		tmp = fma(Float64(z / fma(fma(Float64(y / t), b, a), t, t)), y, Float64(x / fma(Float64(y / t), b, Float64(a - -1.0))));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(fma(t, x, Float64(y * z)) / b) / y);
	elseif (t_1 <= Inf)
		tmp = Float64(fma(Float64(y / t), z, x) / fma(fma(b, y, t), Float64(1.0 / t), a));
	else
		tmp = Float64(fma(Float64(x / y), t, z) / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-303], N[(N[(z / N[(N[(N[(y / t), $MachinePrecision] * b + a), $MachinePrecision] * t + t), $MachinePrecision]), $MachinePrecision] * y + N[(x / N[(N[(y / t), $MachinePrecision] * b + N[(a - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(N[(t * x + N[(y * z), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision] / N[(N[(b * y + t), $MachinePrecision] * N[(1.0 / t), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / y), $MachinePrecision] * t + z), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -4.9999999999999998e-303

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   3. Applied rewrites 76.9%

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

   if -4.9999999999999998e-303 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 26.1%

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

   6. Applied rewrites 32.4%

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

   if 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   3. Applied rewrites 77.4%

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

   5. Applied rewrites 75.5%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 26.1%

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

   6. Applied rewrites 31.1%

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

   8. Applied rewrites 40.0%

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

Alternative 2: 86.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := \mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-303}:\\ \;\;\;\;t\_2 \cdot \frac{1}{\frac{\mathsf{fma}\left(b, y, t\right)}{t} + a}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(t, x, y \cdot z\right)}{b}}{y}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{t\_2}{\mathsf{fma}\left(\mathsf{fma}\left(b, y, t\right), \frac{1}{t}, a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{x}{y}, t, z\right)}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2 (fma (/ y t) z x)))
   (if (<= t_1 -5e-303)
     (* t_2 (/ 1.0 (+ (/ (fma b y t) t) a)))
     (if (<= t_1 0.0)
       (/ (/ (fma t x (* y z)) b) y)
       (if (<= t_1 INFINITY)
         (/ t_2 (fma (fma b y t) (/ 1.0 t) a))
         (/ (fma (/ x y) t z) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_2 = fma((y / t), z, x);
	double tmp;
	if (t_1 <= -5e-303) {
		tmp = t_2 * (1.0 / ((fma(b, y, t) / t) + a));
	} else if (t_1 <= 0.0) {
		tmp = (fma(t, x, (y * z)) / b) / y;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2 / fma(fma(b, y, t), (1.0 / t), a);
	} else {
		tmp = fma((x / y), t, z) / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_2 = fma(Float64(y / t), z, x)
	tmp = 0.0
	if (t_1 <= -5e-303)
		tmp = Float64(t_2 * Float64(1.0 / Float64(Float64(fma(b, y, t) / t) + a)));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(fma(t, x, Float64(y * z)) / b) / y);
	elseif (t_1 <= Inf)
		tmp = Float64(t_2 / fma(fma(b, y, t), Float64(1.0 / t), a));
	else
		tmp = Float64(fma(Float64(x / y), t, z) / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-303], N[(t$95$2 * N[(1.0 / N[(N[(N[(b * y + t), $MachinePrecision] / t), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(N[(t * x + N[(y * z), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(t$95$2 / N[(N[(b * y + t), $MachinePrecision] * N[(1.0 / t), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / y), $MachinePrecision] * t + z), $MachinePrecision] / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -4.9999999999999998e-303

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   3. Applied rewrites 77.4%

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

   5. Applied rewrites 75.5%

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

   7. Applied rewrites 75.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{t}, z, x\right) \cdot \frac{1}{\frac{\mathsf{fma}\left(b, y, t\right)}{t} + a}} \]

   if -4.9999999999999998e-303 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 26.1%

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

   6. Applied rewrites 32.4%

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

   if 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   3. Applied rewrites 77.4%

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

   5. Applied rewrites 75.5%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 26.1%

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

   6. Applied rewrites 31.1%

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

   8. Applied rewrites 40.0%

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

Alternative 3: 86.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := \mathsf{fma}\left(\frac{y}{t}, z, x\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-303}:\\ \;\;\;\;\frac{t\_2}{\mathsf{fma}\left(\frac{y}{t}, b, a - -1\right)}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(t, x, y \cdot z\right)}{b}}{y}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{t\_2}{\mathsf{fma}\left(\mathsf{fma}\left(b, y, t\right), \frac{1}{t}, a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{x}{y}, t, z\right)}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2 (fma (/ y t) z x)))
   (if (<= t_1 -5e-303)
     (/ t_2 (fma (/ y t) b (- a -1.0)))
     (if (<= t_1 0.0)
       (/ (/ (fma t x (* y z)) b) y)
       (if (<= t_1 INFINITY)
         (/ t_2 (fma (fma b y t) (/ 1.0 t) a))
         (/ (fma (/ x y) t z) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_2 = fma((y / t), z, x);
	double tmp;
	if (t_1 <= -5e-303) {
		tmp = t_2 / fma((y / t), b, (a - -1.0));
	} else if (t_1 <= 0.0) {
		tmp = (fma(t, x, (y * z)) / b) / y;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2 / fma(fma(b, y, t), (1.0 / t), a);
	} else {
		tmp = fma((x / y), t, z) / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_2 = fma(Float64(y / t), z, x)
	tmp = 0.0
	if (t_1 <= -5e-303)
		tmp = Float64(t_2 / fma(Float64(y / t), b, Float64(a - -1.0)));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(fma(t, x, Float64(y * z)) / b) / y);
	elseif (t_1 <= Inf)
		tmp = Float64(t_2 / fma(fma(b, y, t), Float64(1.0 / t), a));
	else
		tmp = Float64(fma(Float64(x / y), t, z) / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-303], N[(t$95$2 / N[(N[(y / t), $MachinePrecision] * b + N[(a - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(N[(t * x + N[(y * z), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(t$95$2 / N[(N[(b * y + t), $MachinePrecision] * N[(1.0 / t), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / y), $MachinePrecision] * t + z), $MachinePrecision] / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -4.9999999999999998e-303

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   3. Applied rewrites 77.4%

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

   if -4.9999999999999998e-303 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 26.1%

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

   6. Applied rewrites 32.4%

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

   if 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   3. Applied rewrites 77.4%

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

   5. Applied rewrites 75.5%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 26.1%

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

   6. Applied rewrites 31.1%

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

   8. Applied rewrites 40.0%

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

Alternative 4: 86.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := \frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{\mathsf{fma}\left(\frac{y}{t}, b, a - -1\right)}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-303}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(t, x, y \cdot z\right)}{b}}{y}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+297}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{x}{y}, t, z\right)}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2 (/ (fma (/ y t) z x) (fma (/ y t) b (- a -1.0)))))
   (if (<= t_1 -5e-303)
     t_2
     (if (<= t_1 0.0)
       (/ (/ (fma t x (* y z)) b) y)
       (if (<= t_1 2e+297) t_2 (/ (fma (/ x y) t z) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_2 = fma((y / t), z, x) / fma((y / t), b, (a - -1.0));
	double tmp;
	if (t_1 <= -5e-303) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = (fma(t, x, (y * z)) / b) / y;
	} else if (t_1 <= 2e+297) {
		tmp = t_2;
	} else {
		tmp = fma((x / y), t, z) / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_2 = Float64(fma(Float64(y / t), z, x) / fma(Float64(y / t), b, Float64(a - -1.0)))
	tmp = 0.0
	if (t_1 <= -5e-303)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(fma(t, x, Float64(y * z)) / b) / y);
	elseif (t_1 <= 2e+297)
		tmp = t_2;
	else
		tmp = Float64(fma(Float64(x / y), t, z) / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision] / N[(N[(y / t), $MachinePrecision] * b + N[(a - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-303], t$95$2, If[LessEqual[t$95$1, 0.0], N[(N[(N[(t * x + N[(y * z), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 2e+297], t$95$2, N[(N[(N[(x / y), $MachinePrecision] * t + z), $MachinePrecision] / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -4.9999999999999998e-303 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2e297

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   3. Applied rewrites 77.4%

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

   if -4.9999999999999998e-303 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 26.1%

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

   6. Applied rewrites 32.4%

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

   if 2e297 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 26.1%

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

   6. Applied rewrites 31.1%

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

   8. Applied rewrites 40.0%

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

Alternative 5: 70.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(\frac{x}{y}, t, z\right)}{b}\\ t_2 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-12}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, x, y \cdot z\right)}{\mathsf{fma}\left(b, y, t\right)}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-127}:\\ \;\;\;\;\frac{t\_2}{1 + a}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+60}:\\ \;\;\;\;\frac{t\_2}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (fma (/ x y) t z) b)) (t_2 (+ x (/ (* y z) t))))
   (if (<= y -1.75e+120)
     t_1
     (if (<= y -5.3e-12)
       (/ (fma t x (* y z)) (fma b y t))
       (if (<= y 1.4e-127)
         (/ t_2 (+ 1.0 a))
         (if (<= y 5.4e+60) (/ t_2 (+ 1.0 (/ (* y b) t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((x / y), t, z) / b;
	double t_2 = x + ((y * z) / t);
	double tmp;
	if (y <= -1.75e+120) {
		tmp = t_1;
	} else if (y <= -5.3e-12) {
		tmp = fma(t, x, (y * z)) / fma(b, y, t);
	} else if (y <= 1.4e-127) {
		tmp = t_2 / (1.0 + a);
	} else if (y <= 5.4e+60) {
		tmp = t_2 / (1.0 + ((y * b) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(Float64(x / y), t, z) / b)
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	tmp = 0.0
	if (y <= -1.75e+120)
		tmp = t_1;
	elseif (y <= -5.3e-12)
		tmp = Float64(fma(t, x, Float64(y * z)) / fma(b, y, t));
	elseif (y <= 1.4e-127)
		tmp = Float64(t_2 / Float64(1.0 + a));
	elseif (y <= 5.4e+60)
		tmp = Float64(t_2 / Float64(1.0 + Float64(Float64(y * b) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x / y), $MachinePrecision] * t + z), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.75e+120], t$95$1, If[LessEqual[y, -5.3e-12], N[(N[(t * x + N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(b * y + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e-127], N[(t$95$2 / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e+60], N[(t$95$2 / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.75000000000000004e120 or 5.3999999999999999e60 < y

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 26.1%

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

   6. Applied rewrites 31.1%

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

   8. Applied rewrites 40.0%

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

   if -1.75000000000000004e120 < y < -5.29999999999999963e-12

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   3. Applied rewrites 65.0%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 49.3%

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

   8. Applied rewrites 49.3%

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

   if -5.29999999999999963e-12 < y < 1.4e-127

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 57.3%

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

   if 1.4e-127 < y < 5.3999999999999999e60

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 46.8%

      \[\leadsto \frac{x + \frac{y \cdot z}{t}}{\color{blue}{1} + \frac{y \cdot b}{t}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 69.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(\frac{x}{y}, t, z\right)}{b}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-12}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, x, y \cdot z\right)}{\mathsf{fma}\left(b, y, t\right)}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+82}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (fma (/ x y) t z) b)))
   (if (<= y -1.75e+120)
     t_1
     (if (<= y -5.3e-12)
       (/ (fma t x (* y z)) (fma b y t))
       (if (<= y 9.6e+82) (/ (fma (/ y t) z x) (+ 1.0 a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((x / y), t, z) / b;
	double tmp;
	if (y <= -1.75e+120) {
		tmp = t_1;
	} else if (y <= -5.3e-12) {
		tmp = fma(t, x, (y * z)) / fma(b, y, t);
	} else if (y <= 9.6e+82) {
		tmp = fma((y / t), z, x) / (1.0 + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(Float64(x / y), t, z) / b)
	tmp = 0.0
	if (y <= -1.75e+120)
		tmp = t_1;
	elseif (y <= -5.3e-12)
		tmp = Float64(fma(t, x, Float64(y * z)) / fma(b, y, t));
	elseif (y <= 9.6e+82)
		tmp = Float64(fma(Float64(y / t), z, x) / Float64(1.0 + a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x / y), $MachinePrecision] * t + z), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -1.75e+120], t$95$1, If[LessEqual[y, -5.3e-12], N[(N[(t * x + N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(b * y + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.6e+82], N[(N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision] / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.75000000000000004e120 or 9.59999999999999992e82 < y

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 26.1%

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

   6. Applied rewrites 31.1%

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

   8. Applied rewrites 40.0%

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

   if -1.75000000000000004e120 < y < -5.29999999999999963e-12

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   3. Applied rewrites 65.0%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 49.3%

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

   8. Applied rewrites 49.3%

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

   if -5.29999999999999963e-12 < y < 9.59999999999999992e82

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   3. Applied rewrites 77.4%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 58.9%

      \[\leadsto \frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{\color{blue}{1 + a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 68.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(\frac{x}{y}, t, z\right)}{b}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+82}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (fma (/ x y) t z) b)))
   (if (<= y -1.15e+16)
     t_1
     (if (<= y 9.6e+82) (/ (fma (/ y t) z x) (+ 1.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((x / y), t, z) / b;
	double tmp;
	if (y <= -1.15e+16) {
		tmp = t_1;
	} else if (y <= 9.6e+82) {
		tmp = fma((y / t), z, x) / (1.0 + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(Float64(x / y), t, z) / b)
	tmp = 0.0
	if (y <= -1.15e+16)
		tmp = t_1;
	elseif (y <= 9.6e+82)
		tmp = Float64(fma(Float64(y / t), z, x) / Float64(1.0 + a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x / y), $MachinePrecision] * t + z), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -1.15e+16], t$95$1, If[LessEqual[y, 9.6e+82], N[(N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision] / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e16 or 9.59999999999999992e82 < y

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 26.1%

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

   6. Applied rewrites 31.1%

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

   8. Applied rewrites 40.0%

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

   if -1.15e16 < y < 9.59999999999999992e82

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   3. Applied rewrites 77.4%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 58.9%

      \[\leadsto \frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{\color{blue}{1 + a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 60.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(\frac{x}{y}, t, z\right)}{b}\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 650000000:\\ \;\;\;\;\frac{x}{a - -1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (fma (/ x y) t z) b)))
   (if (<= y -6.8e+15) t_1 (if (<= y 650000000.0) (/ x (- a -1.0)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((x / y), t, z) / b;
	double tmp;
	if (y <= -6.8e+15) {
		tmp = t_1;
	} else if (y <= 650000000.0) {
		tmp = x / (a - -1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(Float64(x / y), t, z) / b)
	tmp = 0.0
	if (y <= -6.8e+15)
		tmp = t_1;
	elseif (y <= 650000000.0)
		tmp = Float64(x / Float64(a - -1.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x / y), $MachinePrecision] * t + z), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -6.8e+15], t$95$1, If[LessEqual[y, 650000000.0], N[(x / N[(a - -1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8e15 or 6.5e8 < y

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 26.1%

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

   6. Applied rewrites 31.1%

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

   8. Applied rewrites 40.0%

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

   if -6.8e15 < y < 6.5e8

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

   4. Applied rewrites 42.6%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

   6. Applied rewrites 42.6%

      \[\leadsto \color{blue}{\frac{x}{a - -1}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 55.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 275000000000:\\ \;\;\;\;\frac{x}{a - -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.8e+15)
   (/ z b)
   (if (<= y 275000000000.0) (/ x (- a -1.0)) (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.8e+15) {
		tmp = z / b;
	} else if (y <= 275000000000.0) {
		tmp = x / (a - -1.0);
	} else {
		tmp = z / b;
	}
	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)
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) :: tmp
    if (y <= (-6.8d+15)) then
        tmp = z / b
    else if (y <= 275000000000.0d0) then
        tmp = x / (a - (-1.0d0))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.8e+15) {
		tmp = z / b;
	} else if (y <= 275000000000.0) {
		tmp = x / (a - -1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.8e+15:
		tmp = z / b
	elif y <= 275000000000.0:
		tmp = x / (a - -1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.8e+15)
		tmp = Float64(z / b);
	elseif (y <= 275000000000.0)
		tmp = Float64(x / Float64(a - -1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -6.8e+15)
		tmp = z / b;
	elseif (y <= 275000000000.0)
		tmp = x / (a - -1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.8e+15], N[(z / b), $MachinePrecision], If[LessEqual[y, 275000000000.0], N[(x / N[(a - -1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8e15 or 2.75e11 < y

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 33.7%

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

   if -6.8e15 < y < 2.75e11

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

   4. Applied rewrites 42.6%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

   6. Applied rewrites 42.6%

      \[\leadsto \color{blue}{\frac{x}{a - -1}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 41.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-12}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-126}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.8e-12) (/ z b) (if (<= y 8.2e-126) (/ x a) (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.8e-12) {
		tmp = z / b;
	} else if (y <= 8.2e-126) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	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)
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) :: tmp
    if (y <= (-4.8d-12)) then
        tmp = z / b
    else if (y <= 8.2d-126) then
        tmp = x / a
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.8e-12) {
		tmp = z / b;
	} else if (y <= 8.2e-126) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.8e-12:
		tmp = z / b
	elif y <= 8.2e-126:
		tmp = x / a
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.8e-12)
		tmp = Float64(z / b);
	elseif (y <= 8.2e-126)
		tmp = Float64(x / a);
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.8e-12)
		tmp = z / b;
	elseif (y <= 8.2e-126)
		tmp = x / a;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.8e-12], N[(z / b), $MachinePrecision], If[LessEqual[y, 8.2e-126], N[(x / a), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.79999999999999974e-12 or 8.1999999999999995e-126 < y

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 33.7%

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

   if -4.79999999999999974e-12 < y < 8.1999999999999995e-126

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

   4. Applied rewrites 42.6%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 25.7%

      \[\leadsto \frac{x}{\color{blue}{a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 25.7% accurate, 5.8× speedup

Math

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

FPCore

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

C

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

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)
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
    code = x / a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / a), $MachinePrecision]

Derivation

1. Initial program 76.1%

   \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

2. Taylor expanded in y around 0

   \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

4. Applied rewrites 42.6%

   \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

5. Taylor expanded in a around inf

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

7. Applied rewrites 25.7%

   \[\leadsto \frac{x}{\color{blue}{a}} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025161 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64
  (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))