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

Percentage Accurate: 75.4% → 89.6%

Time: 5.6s

Alternatives: 17

Speedup: 0.5×

Specification

Math

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

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: 75.4% accurate, 1.0× speedup

Math

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

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: 89.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_3 := 1 + \left(a + \frac{b \cdot y}{t}\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot t\_3} + \frac{y}{t \cdot t\_3}\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+301}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (+ x (/ (* y z) t)))
       (t_2 (/ t_1 (+ (+ a 1.0) (/ (* y b) t))))
       (t_3 (+ 1.0 (+ a (/ (* b y) t)))))
  (if (<= t_2 (- INFINITY))
    (* z (+ (/ x (* z t_3)) (/ y (* t t_3))))
    (if (<= t_2 2e+301) (/ t_1 (+ (+ a 1.0) (* (/ y t) b))) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double t_3 = 1.0 + (a + ((b * y) / t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)));
	} else if (t_2 <= 2e+301) {
		tmp = t_1 / ((a + 1.0) + ((y / t) * b));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double t_3 = 1.0 + (a + ((b * y) / t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)));
	} else if (t_2 <= 2e+301) {
		tmp = t_1 / ((a + 1.0) + ((y / t) * b));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = t_1 / ((a + 1.0) + ((y * b) / t))
	t_3 = 1.0 + (a + ((b * y) / t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)))
	elif t_2 <= 2e+301:
		tmp = t_1 / ((a + 1.0) + ((y / t) * b))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_3 = Float64(1.0 + Float64(a + Float64(Float64(b * y) / t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(x / Float64(z * t_3)) + Float64(y / Float64(t * t_3))));
	elseif (t_2 <= 2e+301)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y / t) * b)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	t_3 = 1.0 + (a + ((b * y) / t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)));
	elseif (t_2 <= 2e+301)
		tmp = t_1 / ((a + 1.0) + ((y / t) * b));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(a + N[(N[(b * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(z * N[(N[(x / N[(z * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+301], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / 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))) < -inf.0

   1. Initial program 75.4%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

   4. Applied rewrites 70.8%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e301

   1. Initial program 75.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 75.1%

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

   3. Applied rewrites 75.1%

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

   if 2.0000000000000001e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 75.4%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   3. Step-by-step derivation

      1. lower-/.f64 34.2%

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

   4. Applied rewrites 34.2%

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

Alternative 2: 89.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;z \cdot \frac{y}{b \cdot y - -1 \cdot \left(t \cdot \left(1 + a\right)\right)}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+301}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (+ x (/ (* y z) t)))
       (t_2 (/ t_1 (+ (+ a 1.0) (/ (* y b) t)))))
  (if (<= t_2 (- INFINITY))
    (* z (/ y (- (* b y) (* -1.0 (* t (+ 1.0 a))))))
    (if (<= t_2 2e+301) (/ t_1 (+ (+ a 1.0) (* (/ y t) b))) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z * (y / ((b * y) - (-1.0 * (t * (1.0 + a)))));
	} else if (t_2 <= 2e+301) {
		tmp = t_1 / ((a + 1.0) + ((y / t) * b));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = z * (y / ((b * y) - (-1.0 * (t * (1.0 + a)))));
	} else if (t_2 <= 2e+301) {
		tmp = t_1 / ((a + 1.0) + ((y / t) * b));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = t_1 / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = z * (y / ((b * y) - (-1.0 * (t * (1.0 + a)))))
	elif t_2 <= 2e+301:
		tmp = t_1 / ((a + 1.0) + ((y / t) * b))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(z * Float64(y / Float64(Float64(b * y) - Float64(-1.0 * Float64(t * Float64(1.0 + a))))));
	elseif (t_2 <= 2e+301)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y / t) * b)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = z * (y / ((b * y) - (-1.0 * (t * (1.0 + a)))));
	elseif (t_2 <= 2e+301)
		tmp = t_1 / ((a + 1.0) + ((y / t) * b));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(z * N[(y / N[(N[(b * y), $MachinePrecision] - N[(-1.0 * N[(t * N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+301], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / 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))) < -inf.0

   1. Initial program 75.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. add-to-fraction N/A

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

      5. associate-/r/ N/A

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

      6. lower-*.f64 N/A

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

   3. Applied rewrites 51.4%

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

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{b \cdot y - -1 \cdot \left(t \cdot \left(1 + a\right)\right)} + \frac{t \cdot x}{z \cdot \left(b \cdot y - -1 \cdot \left(t \cdot \left(1 + a\right)\right)\right)}\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

   6. Applied rewrites 66.6%

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

   7. Taylor expanded in x around 0

      \[\leadsto z \cdot \frac{y}{\color{blue}{b \cdot y - -1 \cdot \left(t \cdot \left(1 + a\right)\right)}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-+.f64 45.5%

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

   9. Applied rewrites 45.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e301

   1. Initial program 75.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 75.1%

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

   3. Applied rewrites 75.1%

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

   if 2.0000000000000001e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 75.4%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   3. Step-by-step derivation

      1. lower-/.f64 34.2%

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

   4. Applied rewrites 34.2%

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

Alternative 3: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \left(a + 1\right) + \frac{y \cdot b}{t}\\ \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{t\_1} \leq 2 \cdot 10^{+301}:\\ \;\;\;\;\frac{x + \frac{y}{t} \cdot z}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (+ (+ a 1.0) (/ (* y b) t))))
  (if (<= (/ (+ x (/ (* y z) t)) t_1) 2e+301)
    (/ (+ x (* (/ y t) z)) t_1)
    (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + ((y * b) / t);
	double tmp;
	if (((x + ((y * z) / t)) / t_1) <= 2e+301) {
		tmp = (x + ((y / t) * z)) / t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (a + 1.0d0) + ((y * b) / t)
    if (((x + ((y * z) / t)) / t_1) <= 2d+301) then
        tmp = (x + ((y / t) * z)) / t_1
    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 t_1 = (a + 1.0) + ((y * b) / t);
	double tmp;
	if (((x + ((y * z) / t)) / t_1) <= 2e+301) {
		tmp = (x + ((y / t) * z)) / t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + 1.0) + ((y * b) / t)
	tmp = 0
	if ((x + ((y * z) / t)) / t_1) <= 2e+301:
		tmp = (x + ((y / t) * z)) / t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t))
	tmp = 0.0
	if (Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1) <= 2e+301)
		tmp = Float64(Float64(x + Float64(Float64(y / t) * z)) / t_1);
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + 1.0) + ((y * b) / t);
	tmp = 0.0;
	if (((x + ((y * z) / t)) / t_1) <= 2e+301)
		tmp = (x + ((y / t) * z)) / t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], 2e+301], N[(N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e301

   1. Initial program 75.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 75.0%

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

   3. Applied rewrites 75.0%

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

   if 2.0000000000000001e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 75.4%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   3. Step-by-step derivation

      1. lower-/.f64 34.2%

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

   4. Applied rewrites 34.2%

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

Alternative 4: 81.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;z \cdot \frac{y}{b \cdot y - -1 \cdot \left(t \cdot \left(1 + a\right)\right)}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+301}:\\ \;\;\;\;\frac{t}{b \cdot y - \left(-1 - a\right) \cdot t} \cdot \left(\frac{z \cdot y}{t} + x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

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 (- INFINITY))
    (* z (/ y (- (* b y) (* -1.0 (* t (+ 1.0 a))))))
    (if (<= t_1 2e+301)
      (* (/ t (- (* b y) (* (- -1.0 a) t))) (+ (/ (* z y) t) x))
      (/ 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 <= -((double) INFINITY)) {
		tmp = z * (y / ((b * y) - (-1.0 * (t * (1.0 + a)))));
	} else if (t_1 <= 2e+301) {
		tmp = (t / ((b * y) - ((-1.0 - a) * t))) * (((z * y) / t) + x);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static 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 <= -Double.POSITIVE_INFINITY) {
		tmp = z * (y / ((b * y) - (-1.0 * (t * (1.0 + a)))));
	} else if (t_1 <= 2e+301) {
		tmp = (t / ((b * y) - ((-1.0 - a) * t))) * (((z * y) / t) + x);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = z * (y / ((b * y) - (-1.0 * (t * (1.0 + a)))))
	elif t_1 <= 2e+301:
		tmp = (t / ((b * y) - ((-1.0 - a) * t))) * (((z * y) / t) + x)
	else:
		tmp = 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 <= Float64(-Inf))
		tmp = Float64(z * Float64(y / Float64(Float64(b * y) - Float64(-1.0 * Float64(t * Float64(1.0 + a))))));
	elseif (t_1 <= 2e+301)
		tmp = Float64(Float64(t / Float64(Float64(b * y) - Float64(Float64(-1.0 - a) * t))) * Float64(Float64(Float64(z * y) / t) + x));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = z * (y / ((b * y) - (-1.0 * (t * (1.0 + a)))));
	elseif (t_1 <= 2e+301)
		tmp = (t / ((b * y) - ((-1.0 - a) * t))) * (((z * y) / t) + x);
	else
		tmp = z / b;
	end
	tmp_2 = 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, (-Infinity)], N[(z * N[(y / N[(N[(b * y), $MachinePrecision] - N[(-1.0 * N[(t * N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+301], N[(N[(t / N[(N[(b * y), $MachinePrecision] - N[(N[(-1.0 - a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(z / 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))) < -inf.0

   1. Initial program 75.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. add-to-fraction N/A

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

      5. associate-/r/ N/A

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

      6. lower-*.f64 N/A

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

   3. Applied rewrites 51.4%

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

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{b \cdot y - -1 \cdot \left(t \cdot \left(1 + a\right)\right)} + \frac{t \cdot x}{z \cdot \left(b \cdot y - -1 \cdot \left(t \cdot \left(1 + a\right)\right)\right)}\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

   6. Applied rewrites 66.6%

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

   7. Taylor expanded in x around 0

      \[\leadsto z \cdot \frac{y}{\color{blue}{b \cdot y - -1 \cdot \left(t \cdot \left(1 + a\right)\right)}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-+.f64 45.5%

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

   9. Applied rewrites 45.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e301

   1. Initial program 75.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   3. Applied rewrites 68.2%

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

   if 2.0000000000000001e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 75.4%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   3. Step-by-step derivation

      1. lower-/.f64 34.2%

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

   4. Applied rewrites 34.2%

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

Alternative 5: 79.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;z \cdot \frac{y}{b \cdot y - -1 \cdot \left(t \cdot \left(1 + a\right)\right)}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+172}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+301}:\\ \;\;\;\;\frac{t \cdot x + z \cdot y}{a \cdot t + \left(b \cdot y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

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 (- INFINITY))
    (* z (/ y (- (* b y) (* -1.0 (* t (+ 1.0 a))))))
    (if (<= t_1 -5e+172)
      (/ x (+ 1.0 (+ a (/ (* b y) t))))
      (if (<= t_1 2e+301)
        (/ (+ (* t x) (* z y)) (+ (* a t) (+ (* b 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 <= -((double) INFINITY)) {
		tmp = z * (y / ((b * y) - (-1.0 * (t * (1.0 + a)))));
	} else if (t_1 <= -5e+172) {
		tmp = x / (1.0 + (a + ((b * y) / t)));
	} else if (t_1 <= 2e+301) {
		tmp = ((t * x) + (z * y)) / ((a * t) + ((b * y) + t));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static 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 <= -Double.POSITIVE_INFINITY) {
		tmp = z * (y / ((b * y) - (-1.0 * (t * (1.0 + a)))));
	} else if (t_1 <= -5e+172) {
		tmp = x / (1.0 + (a + ((b * y) / t)));
	} else if (t_1 <= 2e+301) {
		tmp = ((t * x) + (z * y)) / ((a * t) + ((b * y) + t));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = z * (y / ((b * y) - (-1.0 * (t * (1.0 + a)))))
	elif t_1 <= -5e+172:
		tmp = x / (1.0 + (a + ((b * y) / t)))
	elif t_1 <= 2e+301:
		tmp = ((t * x) + (z * y)) / ((a * t) + ((b * y) + t))
	else:
		tmp = 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 <= Float64(-Inf))
		tmp = Float64(z * Float64(y / Float64(Float64(b * y) - Float64(-1.0 * Float64(t * Float64(1.0 + a))))));
	elseif (t_1 <= -5e+172)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(b * y) / t))));
	elseif (t_1 <= 2e+301)
		tmp = Float64(Float64(Float64(t * x) + Float64(z * y)) / Float64(Float64(a * t) + Float64(Float64(b * y) + t)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = z * (y / ((b * y) - (-1.0 * (t * (1.0 + a)))));
	elseif (t_1 <= -5e+172)
		tmp = x / (1.0 + (a + ((b * y) / t)));
	elseif (t_1 <= 2e+301)
		tmp = ((t * x) + (z * y)) / ((a * t) + ((b * y) + t));
	else
		tmp = z / b;
	end
	tmp_2 = 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, (-Infinity)], N[(z * N[(y / N[(N[(b * y), $MachinePrecision] - N[(-1.0 * N[(t * N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+172], N[(x / N[(1.0 + N[(a + N[(N[(b * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+301], N[(N[(N[(t * x), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(a * t), $MachinePrecision] + N[(N[(b * y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / 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))) < -inf.0

   1. Initial program 75.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. add-to-fraction N/A

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

      5. associate-/r/ N/A

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

      6. lower-*.f64 N/A

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

   3. Applied rewrites 51.4%

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

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{b \cdot y - -1 \cdot \left(t \cdot \left(1 + a\right)\right)} + \frac{t \cdot x}{z \cdot \left(b \cdot y - -1 \cdot \left(t \cdot \left(1 + a\right)\right)\right)}\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

   6. Applied rewrites 66.6%

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

   7. Taylor expanded in x around 0

      \[\leadsto z \cdot \frac{y}{\color{blue}{b \cdot y - -1 \cdot \left(t \cdot \left(1 + a\right)\right)}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-+.f64 45.5%

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

   9. Applied rewrites 45.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -5.0000000000000001e172

   1. Initial program 75.4%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 42.6%

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

   4. Applied rewrites 42.6%

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

   5. Taylor expanded in a around inf

      \[\leadsto \frac{x}{\color{blue}{a}} \]
   6. Step-by-step derivation

      1. lower-/.f64 26.1%

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

   7. Applied rewrites 26.1%

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

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 52.2%

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

   10. Applied rewrites 52.2%

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

   if -5.0000000000000001e172 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e301

   1. Initial program 75.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. add-to-fraction N/A

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

      5. associate-/l/ N/A

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

      6. lower-/.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift-+.f64 N/A

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

      14. lift-+.f64 N/A

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

      15. associate-+l+ N/A

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

      16. distribute-rgt-in N/A

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

      17. lower-+.f64 N/A

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

      18. lower-*.f64 N/A

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

      19. lower-*.f64 N/A

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

   3. Applied rewrites 70.9%

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

   if 2.0000000000000001e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 75.4%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   3. Step-by-step derivation

      1. lower-/.f64 34.2%

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

   4. Applied rewrites 34.2%

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

Alternative 6: 73.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{1 + a}\\ t_3 := \frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;z \cdot \frac{y}{b \cdot y - -1 \cdot \left(t \cdot \left(1 + a\right)\right)}\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-211}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)}\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+301}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (+ x (/ (* y z) t)))
       (t_2 (/ t_1 (+ 1.0 a)))
       (t_3 (/ t_1 (+ (+ a 1.0) (/ (* y b) t)))))
  (if (<= t_3 (- INFINITY))
    (* z (/ y (- (* b y) (* -1.0 (* t (+ 1.0 a))))))
    (if (<= t_3 -2e-211)
      t_2
      (if (<= t_3 0.0)
        (/ x (+ 1.0 (+ a (/ (* b y) t))))
        (if (<= t_3 2e+301) t_2 (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / (1.0 + a);
	double t_3 = t_1 / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = z * (y / ((b * y) - (-1.0 * (t * (1.0 + a)))));
	} else if (t_3 <= -2e-211) {
		tmp = t_2;
	} else if (t_3 <= 0.0) {
		tmp = x / (1.0 + (a + ((b * y) / t)));
	} else if (t_3 <= 2e+301) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / (1.0 + a);
	double t_3 = t_1 / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = z * (y / ((b * y) - (-1.0 * (t * (1.0 + a)))));
	} else if (t_3 <= -2e-211) {
		tmp = t_2;
	} else if (t_3 <= 0.0) {
		tmp = x / (1.0 + (a + ((b * y) / t)));
	} else if (t_3 <= 2e+301) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = t_1 / (1.0 + a)
	t_3 = t_1 / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = z * (y / ((b * y) - (-1.0 * (t * (1.0 + a)))))
	elif t_3 <= -2e-211:
		tmp = t_2
	elif t_3 <= 0.0:
		tmp = x / (1.0 + (a + ((b * y) / t)))
	elif t_3 <= 2e+301:
		tmp = t_2
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(1.0 + a))
	t_3 = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(z * Float64(y / Float64(Float64(b * y) - Float64(-1.0 * Float64(t * Float64(1.0 + a))))));
	elseif (t_3 <= -2e-211)
		tmp = t_2;
	elseif (t_3 <= 0.0)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(b * y) / t))));
	elseif (t_3 <= 2e+301)
		tmp = t_2;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	t_2 = t_1 / (1.0 + a);
	t_3 = t_1 / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = z * (y / ((b * y) - (-1.0 * (t * (1.0 + a)))));
	elseif (t_3 <= -2e-211)
		tmp = t_2;
	elseif (t_3 <= 0.0)
		tmp = x / (1.0 + (a + ((b * y) / t)));
	elseif (t_3 <= 2e+301)
		tmp = t_2;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(z * N[(y / N[(N[(b * y), $MachinePrecision] - N[(-1.0 * N[(t * N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -2e-211], t$95$2, If[LessEqual[t$95$3, 0.0], N[(x / N[(1.0 + N[(a + N[(N[(b * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+301], t$95$2, N[(z / 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))) < -inf.0

   1. Initial program 75.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. add-to-fraction N/A

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

      5. associate-/r/ N/A

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

      6. lower-*.f64 N/A

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

   3. Applied rewrites 51.4%

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

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{b \cdot y - -1 \cdot \left(t \cdot \left(1 + a\right)\right)} + \frac{t \cdot x}{z \cdot \left(b \cdot y - -1 \cdot \left(t \cdot \left(1 + a\right)\right)\right)}\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

   6. Applied rewrites 66.6%

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

   7. Taylor expanded in x around 0

      \[\leadsto z \cdot \frac{y}{\color{blue}{b \cdot y - -1 \cdot \left(t \cdot \left(1 + a\right)\right)}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-+.f64 45.5%

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

   9. Applied rewrites 45.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -2.0000000000000002e-211 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e301

   1. Initial program 75.4%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 56.8%

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

   4. Applied rewrites 56.8%

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

   if -2.0000000000000002e-211 < (/.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 75.4%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 42.6%

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

   4. Applied rewrites 42.6%

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

   5. Taylor expanded in a around inf

      \[\leadsto \frac{x}{\color{blue}{a}} \]
   6. Step-by-step derivation

      1. lower-/.f64 26.1%

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

   7. Applied rewrites 26.1%

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

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 52.2%

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

   10. Applied rewrites 52.2%

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

   if 2.0000000000000001e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 75.4%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   3. Step-by-step derivation

      1. lower-/.f64 34.2%

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

   4. Applied rewrites 34.2%

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

Alternative 7: 72.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{1 + a}\\ t_3 := \frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;\frac{\frac{x \cdot t}{y} + z}{b}\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-211}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)}\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+301}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (+ x (/ (* y z) t)))
       (t_2 (/ t_1 (+ 1.0 a)))
       (t_3 (/ t_1 (+ (+ a 1.0) (/ (* y b) t)))))
  (if (<= t_3 (- INFINITY))
    (/ (+ (/ (* x t) y) z) b)
    (if (<= t_3 -2e-211)
      t_2
      (if (<= t_3 0.0)
        (/ x (+ 1.0 (+ a (/ (* b y) t))))
        (if (<= t_3 2e+301) t_2 (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / (1.0 + a);
	double t_3 = t_1 / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = (((x * t) / y) + z) / b;
	} else if (t_3 <= -2e-211) {
		tmp = t_2;
	} else if (t_3 <= 0.0) {
		tmp = x / (1.0 + (a + ((b * y) / t)));
	} else if (t_3 <= 2e+301) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / (1.0 + a);
	double t_3 = t_1 / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = (((x * t) / y) + z) / b;
	} else if (t_3 <= -2e-211) {
		tmp = t_2;
	} else if (t_3 <= 0.0) {
		tmp = x / (1.0 + (a + ((b * y) / t)));
	} else if (t_3 <= 2e+301) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = t_1 / (1.0 + a)
	t_3 = t_1 / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = (((x * t) / y) + z) / b
	elif t_3 <= -2e-211:
		tmp = t_2
	elif t_3 <= 0.0:
		tmp = x / (1.0 + (a + ((b * y) / t)))
	elif t_3 <= 2e+301:
		tmp = t_2
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(1.0 + a))
	t_3 = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(x * t) / y) + z) / b);
	elseif (t_3 <= -2e-211)
		tmp = t_2;
	elseif (t_3 <= 0.0)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(b * y) / t))));
	elseif (t_3 <= 2e+301)
		tmp = t_2;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	t_2 = t_1 / (1.0 + a);
	t_3 = t_1 / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = (((x * t) / y) + z) / b;
	elseif (t_3 <= -2e-211)
		tmp = t_2;
	elseif (t_3 <= 0.0)
		tmp = x / (1.0 + (a + ((b * y) / t)));
	elseif (t_3 <= 2e+301)
		tmp = t_2;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision] + z), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$3, -2e-211], t$95$2, If[LessEqual[t$95$3, 0.0], N[(x / N[(1.0 + N[(a + N[(N[(b * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+301], t$95$2, N[(z / 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))) < -inf.0

   1. Initial program 75.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. add-to-fraction N/A

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

      5. associate-/r/ N/A

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

      6. lower-*.f64 N/A

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

   3. Applied rewrites 51.4%

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

   4. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{t \cdot x + y \cdot z}{b \cdot y}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 31.0%

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

   6. Applied rewrites 31.0%

      \[\leadsto \color{blue}{\frac{t \cdot x + y \cdot z}{b \cdot y}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. times-frac N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift-+.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 N/A

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

      24. lower-/.f64 34.9%

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

   8. Applied rewrites 34.9%

      \[\leadsto \frac{z \cdot y + x \cdot t}{y} \cdot \color{blue}{\frac{1}{b}} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip-rev N/A

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

      4. lower-/.f64 35.0%

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

      5. lift-/.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. add-to-fraction-rev N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lower-/.f64 40.5%

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lift-*.f64 40.5%

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

   10. Applied rewrites 40.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -2.0000000000000002e-211 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e301

   1. Initial program 75.4%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 56.8%

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

   4. Applied rewrites 56.8%

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

   if -2.0000000000000002e-211 < (/.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 75.4%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 42.6%

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

   4. Applied rewrites 42.6%

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

   5. Taylor expanded in a around inf

      \[\leadsto \frac{x}{\color{blue}{a}} \]
   6. Step-by-step derivation

      1. lower-/.f64 26.1%

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

   7. Applied rewrites 26.1%

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

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 52.2%

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

   10. Applied rewrites 52.2%

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

   if 2.0000000000000001e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 75.4%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   3. Step-by-step derivation

      1. lower-/.f64 34.2%

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

   4. Applied rewrites 34.2%

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

Alternative 8: 69.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \frac{x + \left(-z\right) \cdot \left(y \cdot \frac{-1}{t}\right)}{1 + a}\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+61}:\\ \;\;\;\;\frac{t \cdot x + y \cdot z}{b \cdot y - -1 \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (/ (+ x (* (- z) (* y (/ -1.0 t)))) (+ 1.0 a))))
  (if (<= a -1.75e+18)
    t_1
    (if (<= a 4.5e+61)
      (/ (+ (* t x) (* y z)) (- (* b y) (* -1.0 t)))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (-z * (y * (-1.0 / t)))) / (1.0 + a);
	double tmp;
	if (a <= -1.75e+18) {
		tmp = t_1;
	} else if (a <= 4.5e+61) {
		tmp = ((t * x) + (y * z)) / ((b * y) - (-1.0 * t));
	} 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)
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) :: t_1
    real(8) :: tmp
    t_1 = (x + (-z * (y * ((-1.0d0) / t)))) / (1.0d0 + a)
    if (a <= (-1.75d+18)) then
        tmp = t_1
    else if (a <= 4.5d+61) then
        tmp = ((t * x) + (y * z)) / ((b * y) - ((-1.0d0) * t))
    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 t_1 = (x + (-z * (y * (-1.0 / t)))) / (1.0 + a);
	double tmp;
	if (a <= -1.75e+18) {
		tmp = t_1;
	} else if (a <= 4.5e+61) {
		tmp = ((t * x) + (y * z)) / ((b * y) - (-1.0 * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (-z * (y * (-1.0 / t)))) / (1.0 + a)
	tmp = 0
	if a <= -1.75e+18:
		tmp = t_1
	elif a <= 4.5e+61:
		tmp = ((t * x) + (y * z)) / ((b * y) - (-1.0 * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(-z) * Float64(y * Float64(-1.0 / t)))) / Float64(1.0 + a))
	tmp = 0.0
	if (a <= -1.75e+18)
		tmp = t_1;
	elseif (a <= 4.5e+61)
		tmp = Float64(Float64(Float64(t * x) + Float64(y * z)) / Float64(Float64(b * y) - Float64(-1.0 * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (-z * (y * (-1.0 / t)))) / (1.0 + a);
	tmp = 0.0;
	if (a <= -1.75e+18)
		tmp = t_1;
	elseif (a <= 4.5e+61)
		tmp = ((t * x) + (y * z)) / ((b * y) - (-1.0 * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[((-z) * N[(y * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.75e+18], t$95$1, If[LessEqual[a, 4.5e+61], N[(N[(N[(t * x), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(N[(b * y), $MachinePrecision] - N[(-1.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.75e18 or 4.5e61 < a

   1. Initial program 75.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. mult-flip N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. distribute-lft-neg-in N/A

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

      7. associate-*l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. distribute-neg-frac2 N/A

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

      12. distribute-neg-frac N/A

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

      13. lower-/.f64 N/A

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

      14. metadata-eval 75.0%

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

   3. Applied rewrites 75.0%

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

   4. Taylor expanded in y around 0

      \[\leadsto \frac{x + \left(-z\right) \cdot \left(y \cdot \frac{-1}{t}\right)}{\color{blue}{1 + a}} \]
   5. Step-by-step derivation

      1. lower-+.f64 58.4%

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

   6. Applied rewrites 58.4%

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

   if -1.75e18 < a < 4.5e61

   1. Initial program 75.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. add-to-fraction N/A

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

      5. associate-/r/ N/A

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

      6. lower-*.f64 N/A

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

   3. Applied rewrites 51.4%

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

   4. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{t \cdot x + y \cdot z}{b \cdot y}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 31.0%

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

   6. Applied rewrites 31.0%

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

   7. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t \cdot x + y \cdot z}{b \cdot y - -1 \cdot t}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 49.8%

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

   9. Applied rewrites 49.8%

      \[\leadsto \color{blue}{\frac{t \cdot x + y \cdot z}{b \cdot y - -1 \cdot t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 64.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{\frac{x \cdot t}{y} + z}{b}\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-89}:\\ \;\;\;\;\frac{y \cdot z + t \cdot x}{t \cdot \left(a - -1\right)}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+301}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (/ x (+ 1.0 (+ a (/ (* b y) t)))))
       (t_2 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
  (if (<= t_2 (- INFINITY))
    (/ (+ (/ (* x t) y) z) b)
    (if (<= t_2 -5e+172)
      t_1
      (if (<= t_2 -2e-89)
        (/ (+ (* y z) (* t x)) (* t (- a -1.0)))
        (if (<= t_2 2e+301) t_1 (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (a + ((b * y) / t)));
	double t_2 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (((x * t) / y) + z) / b;
	} else if (t_2 <= -5e+172) {
		tmp = t_1;
	} else if (t_2 <= -2e-89) {
		tmp = ((y * z) + (t * x)) / (t * (a - -1.0));
	} else if (t_2 <= 2e+301) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (a + ((b * y) / t)));
	double t_2 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (((x * t) / y) + z) / b;
	} else if (t_2 <= -5e+172) {
		tmp = t_1;
	} else if (t_2 <= -2e-89) {
		tmp = ((y * z) + (t * x)) / (t * (a - -1.0));
	} else if (t_2 <= 2e+301) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + (a + ((b * y) / t)))
	t_2 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (((x * t) / y) + z) / b
	elif t_2 <= -5e+172:
		tmp = t_1
	elif t_2 <= -2e-89:
		tmp = ((y * z) + (t * x)) / (t * (a - -1.0))
	elif t_2 <= 2e+301:
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(b * y) / t))))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(x * t) / y) + z) / b);
	elseif (t_2 <= -5e+172)
		tmp = t_1;
	elseif (t_2 <= -2e-89)
		tmp = Float64(Float64(Float64(y * z) + Float64(t * x)) / Float64(t * Float64(a - -1.0)));
	elseif (t_2 <= 2e+301)
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + (a + ((b * y) / t)));
	t_2 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (((x * t) / y) + z) / b;
	elseif (t_2 <= -5e+172)
		tmp = t_1;
	elseif (t_2 <= -2e-89)
		tmp = ((y * z) + (t * x)) / (t * (a - -1.0));
	elseif (t_2 <= 2e+301)
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + N[(a + N[(N[(b * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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$2, (-Infinity)], N[(N[(N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision] + z), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$2, -5e+172], t$95$1, If[LessEqual[t$95$2, -2e-89], N[(N[(N[(y * z), $MachinePrecision] + N[(t * x), $MachinePrecision]), $MachinePrecision] / N[(t * N[(a - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+301], t$95$1, N[(z / 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))) < -inf.0

   1. Initial program 75.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. add-to-fraction N/A

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

      5. associate-/r/ N/A

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

      6. lower-*.f64 N/A

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

   3. Applied rewrites 51.4%

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

   4. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{t \cdot x + y \cdot z}{b \cdot y}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 31.0%

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

   6. Applied rewrites 31.0%

      \[\leadsto \color{blue}{\frac{t \cdot x + y \cdot z}{b \cdot y}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. times-frac N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift-+.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 N/A

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

      24. lower-/.f64 34.9%

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

   8. Applied rewrites 34.9%

      \[\leadsto \frac{z \cdot y + x \cdot t}{y} \cdot \color{blue}{\frac{1}{b}} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip-rev N/A

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

      4. lower-/.f64 35.0%

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

      5. lift-/.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. add-to-fraction-rev N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lower-/.f64 40.5%

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lift-*.f64 40.5%

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

   10. Applied rewrites 40.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -5.0000000000000001e172 or -2.0000000000000001e-89 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e301

   1. Initial program 75.4%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 42.6%

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

   4. Applied rewrites 42.6%

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

   5. Taylor expanded in a around inf

      \[\leadsto \frac{x}{\color{blue}{a}} \]
   6. Step-by-step derivation

      1. lower-/.f64 26.1%

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

   7. Applied rewrites 26.1%

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

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 52.2%

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

   10. Applied rewrites 52.2%

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

   if -5.0000000000000001e172 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -2.0000000000000001e-89

   1. Initial program 75.4%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 56.8%

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

   4. Applied rewrites 56.8%

      \[\leadsto \frac{x + \frac{y \cdot z}{t}}{\color{blue}{1 + a}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. add-to-fraction N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. associate-/l/ N/A

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

      12. lower-/.f64 N/A

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

      13. lift-+.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lift-*.f64 N/A

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

      19. lower-*.f64 44.4%

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

      20. lift-+.f64 N/A

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

      21. +-commutative N/A

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

      22. add-flip N/A

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

      23. metadata-eval N/A

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

   6. Applied rewrites 44.4%

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

   if 2.0000000000000001e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 75.4%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   3. Step-by-step derivation

      1. lower-/.f64 34.2%

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

   4. Applied rewrites 34.2%

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

Alternative 10: 60.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-31}:\\ \;\;\;\;\frac{\frac{x \cdot t}{y} + z}{b}\\ \mathbf{elif}\;y \leq 2450000000:\\ \;\;\;\;\frac{y \cdot z + t \cdot x}{t \cdot \left(a - -1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (if (<= y -9.5e-31)
  (/ (+ (/ (* x t) y) z) b)
  (if (<= y 2450000000.0)
    (/ (+ (* y z) (* t x)) (* t (- a -1.0)))
    (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.5e-31) {
		tmp = (((x * t) / y) + z) / b;
	} else if (y <= 2450000000.0) {
		tmp = ((y * z) + (t * x)) / (t * (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 <= (-9.5d-31)) then
        tmp = (((x * t) / y) + z) / b
    else if (y <= 2450000000.0d0) then
        tmp = ((y * z) + (t * x)) / (t * (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 <= -9.5e-31) {
		tmp = (((x * t) / y) + z) / b;
	} else if (y <= 2450000000.0) {
		tmp = ((y * z) + (t * x)) / (t * (a - -1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -9.5e-31:
		tmp = (((x * t) / y) + z) / b
	elif y <= 2450000000.0:
		tmp = ((y * z) + (t * x)) / (t * (a - -1.0))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -9.5e-31)
		tmp = Float64(Float64(Float64(Float64(x * t) / y) + z) / b);
	elseif (y <= 2450000000.0)
		tmp = Float64(Float64(Float64(y * z) + Float64(t * x)) / Float64(t * 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 <= -9.5e-31)
		tmp = (((x * t) / y) + z) / b;
	elseif (y <= 2450000000.0)
		tmp = ((y * z) + (t * x)) / (t * (a - -1.0));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -9.5e-31], N[(N[(N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision] + z), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 2450000000.0], N[(N[(N[(y * z), $MachinePrecision] + N[(t * x), $MachinePrecision]), $MachinePrecision] / N[(t * N[(a - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.5000000000000008e-31

   1. Initial program 75.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. add-to-fraction N/A

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

      5. associate-/r/ N/A

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

      6. lower-*.f64 N/A

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

   3. Applied rewrites 51.4%

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

   4. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{t \cdot x + y \cdot z}{b \cdot y}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 31.0%

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

   6. Applied rewrites 31.0%

      \[\leadsto \color{blue}{\frac{t \cdot x + y \cdot z}{b \cdot y}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. times-frac N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift-+.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 N/A

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

      24. lower-/.f64 34.9%

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

   8. Applied rewrites 34.9%

      \[\leadsto \frac{z \cdot y + x \cdot t}{y} \cdot \color{blue}{\frac{1}{b}} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip-rev N/A

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

      4. lower-/.f64 35.0%

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

      5. lift-/.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. add-to-fraction-rev N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lower-/.f64 40.5%

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lift-*.f64 40.5%

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

   10. Applied rewrites 40.5%

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

   if -9.5000000000000008e-31 < y < 2.45e9

   1. Initial program 75.4%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 56.8%

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

   4. Applied rewrites 56.8%

      \[\leadsto \frac{x + \frac{y \cdot z}{t}}{\color{blue}{1 + a}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. add-to-fraction N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. associate-/l/ N/A

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

      12. lower-/.f64 N/A

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

      13. lift-+.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lift-*.f64 N/A

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

      19. lower-*.f64 44.4%

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

      20. lift-+.f64 N/A

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

      21. +-commutative N/A

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

      22. add-flip N/A

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

      23. metadata-eval N/A

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

   6. Applied rewrites 44.4%

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

   if 2.45e9 < y

   1. Initial program 75.4%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   3. Step-by-step derivation

      1. lower-/.f64 34.2%

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

   4. Applied rewrites 34.2%

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

Alternative 11: 58.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{if}\;a \leq -1650000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+61}:\\ \;\;\;\;\frac{\frac{x \cdot t}{y} + z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (/ (+ x (/ (* y z) t)) a)))
  (if (<= a -1650000.0)
    t_1
    (if (<= a -1.02e-98)
      (/ x (+ 1.0 a))
      (if (<= a 4.5e+61) (/ (+ (/ (* x t) y) z) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / a;
	double tmp;
	if (a <= -1650000.0) {
		tmp = t_1;
	} else if (a <= -1.02e-98) {
		tmp = x / (1.0 + a);
	} else if (a <= 4.5e+61) {
		tmp = (((x * t) / y) + z) / b;
	} 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)
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) :: t_1
    real(8) :: tmp
    t_1 = (x + ((y * z) / t)) / a
    if (a <= (-1650000.0d0)) then
        tmp = t_1
    else if (a <= (-1.02d-98)) then
        tmp = x / (1.0d0 + a)
    else if (a <= 4.5d+61) then
        tmp = (((x * t) / y) + z) / b
    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 t_1 = (x + ((y * z) / t)) / a;
	double tmp;
	if (a <= -1650000.0) {
		tmp = t_1;
	} else if (a <= -1.02e-98) {
		tmp = x / (1.0 + a);
	} else if (a <= 4.5e+61) {
		tmp = (((x * t) / y) + z) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / a
	tmp = 0
	if a <= -1650000.0:
		tmp = t_1
	elif a <= -1.02e-98:
		tmp = x / (1.0 + a)
	elif a <= 4.5e+61:
		tmp = (((x * t) / y) + z) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / a)
	tmp = 0.0
	if (a <= -1650000.0)
		tmp = t_1;
	elseif (a <= -1.02e-98)
		tmp = Float64(x / Float64(1.0 + a));
	elseif (a <= 4.5e+61)
		tmp = Float64(Float64(Float64(Float64(x * t) / y) + z) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / a;
	tmp = 0.0;
	if (a <= -1650000.0)
		tmp = t_1;
	elseif (a <= -1.02e-98)
		tmp = x / (1.0 + a);
	elseif (a <= 4.5e+61)
		tmp = (((x * t) / y) + z) / b;
	else
		tmp = t_1;
	end
	tmp_2 = 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] / a), $MachinePrecision]}, If[LessEqual[a, -1650000.0], t$95$1, If[LessEqual[a, -1.02e-98], N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e+61], N[(N[(N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision] + z), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.65e6 or 4.5e61 < a

   1. Initial program 75.4%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 42.6%

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

   4. Applied rewrites 42.6%

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

   5. Taylor expanded in a around inf

      \[\leadsto \frac{x}{\color{blue}{a}} \]
   6. Step-by-step derivation

      1. lower-/.f64 26.1%

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

   7. Applied rewrites 26.1%

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

   8. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z}{t}}{a}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 34.0%

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

   10. Applied rewrites 34.0%

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

   if -1.65e6 < a < -1.02e-98

   1. Initial program 75.4%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 42.6%

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

   4. Applied rewrites 42.6%

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

   if -1.02e-98 < a < 4.5e61

   1. Initial program 75.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. add-to-fraction N/A

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

      5. associate-/r/ N/A

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

      6. lower-*.f64 N/A

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

   3. Applied rewrites 51.4%

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

   4. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{t \cdot x + y \cdot z}{b \cdot y}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 31.0%

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

   6. Applied rewrites 31.0%

      \[\leadsto \color{blue}{\frac{t \cdot x + y \cdot z}{b \cdot y}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. times-frac N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift-+.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 N/A

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

      24. lower-/.f64 34.9%

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

   8. Applied rewrites 34.9%

      \[\leadsto \frac{z \cdot y + x \cdot t}{y} \cdot \color{blue}{\frac{1}{b}} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip-rev N/A

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

      4. lower-/.f64 35.0%

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

      5. lift-/.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. add-to-fraction-rev N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lower-/.f64 40.5%

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lift-*.f64 40.5%

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

   10. Applied rewrites 40.5%

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

Alternative 12: 56.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{1 + a}\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-77}:\\ \;\;\;\;\frac{\frac{x \cdot t}{y} + z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (/ x (+ 1.0 a))))
  (if (<= t -1.2e-33)
    t_1
    (if (<= t 1.8e-77) (/ (+ (/ (* x t) y) z) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + a);
	double tmp;
	if (t <= -1.2e-33) {
		tmp = t_1;
	} else if (t <= 1.8e-77) {
		tmp = (((x * t) / y) + z) / b;
	} 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)
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) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 + a)
    if (t <= (-1.2d-33)) then
        tmp = t_1
    else if (t <= 1.8d-77) then
        tmp = (((x * t) / y) + z) / b
    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 t_1 = x / (1.0 + a);
	double tmp;
	if (t <= -1.2e-33) {
		tmp = t_1;
	} else if (t <= 1.8e-77) {
		tmp = (((x * t) / y) + z) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + a)
	tmp = 0
	if t <= -1.2e-33:
		tmp = t_1
	elif t <= 1.8e-77:
		tmp = (((x * t) / y) + z) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + a))
	tmp = 0.0
	if (t <= -1.2e-33)
		tmp = t_1;
	elseif (t <= 1.8e-77)
		tmp = Float64(Float64(Float64(Float64(x * t) / y) + z) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + a);
	tmp = 0.0;
	if (t <= -1.2e-33)
		tmp = t_1;
	elseif (t <= 1.8e-77)
		tmp = (((x * t) / y) + z) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e-33], t$95$1, If[LessEqual[t, 1.8e-77], N[(N[(N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision] + z), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2e-33 or 1.8e-77 < t

   1. Initial program 75.4%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 42.6%

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

   4. Applied rewrites 42.6%

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

   if -1.2e-33 < t < 1.8e-77

   1. Initial program 75.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. add-to-fraction N/A

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

      5. associate-/r/ N/A

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

      6. lower-*.f64 N/A

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

   3. Applied rewrites 51.4%

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

   4. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{t \cdot x + y \cdot z}{b \cdot y}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 31.0%

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

   6. Applied rewrites 31.0%

      \[\leadsto \color{blue}{\frac{t \cdot x + y \cdot z}{b \cdot y}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. times-frac N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift-+.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 N/A

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

      24. lower-/.f64 34.9%

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

   8. Applied rewrites 34.9%

      \[\leadsto \frac{z \cdot y + x \cdot t}{y} \cdot \color{blue}{\frac{1}{b}} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip-rev N/A

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

      4. lower-/.f64 35.0%

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

      5. lift-/.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. add-to-fraction-rev N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lower-/.f64 40.5%

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lift-*.f64 40.5%

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

   10. Applied rewrites 40.5%

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

Alternative 13: 54.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+301}:\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

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 (- INFINITY))
    (/ z b)
    (if (<= t_1 2e+301) (/ x (+ 1.0 a)) (/ 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 <= -((double) INFINITY)) {
		tmp = z / b;
	} else if (t_1 <= 2e+301) {
		tmp = x / (1.0 + a);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static 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 <= -Double.POSITIVE_INFINITY) {
		tmp = z / b;
	} else if (t_1 <= 2e+301) {
		tmp = x / (1.0 + a);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = z / b
	elif t_1 <= 2e+301:
		tmp = x / (1.0 + a)
	else:
		tmp = 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 <= Float64(-Inf))
		tmp = Float64(z / b);
	elseif (t_1 <= 2e+301)
		tmp = Float64(x / Float64(1.0 + a));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = z / b;
	elseif (t_1 <= 2e+301)
		tmp = x / (1.0 + a);
	else
		tmp = z / b;
	end
	tmp_2 = 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, (-Infinity)], N[(z / b), $MachinePrecision], If[LessEqual[t$95$1, 2e+301], N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -inf.0 or 2.0000000000000001e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 75.4%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   3. Step-by-step derivation

      1. lower-/.f64 34.2%

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

   4. Applied rewrites 34.2%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e301

   1. Initial program 75.4%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 42.6%

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

   4. Applied rewrites 42.6%

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

Alternative 14: 43.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-161}:\\ \;\;\;\;x + -1 \cdot \left(a \cdot x\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+61}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (if (<= a -4.2e-11)
  (/ x a)
  (if (<= a -8.6e-161)
    (+ x (* -1.0 (* a x)))
    (if (<= a 4.5e+61) (/ z b) (/ x a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.2e-11) {
		tmp = x / a;
	} else if (a <= -8.6e-161) {
		tmp = x + (-1.0 * (a * x));
	} else if (a <= 4.5e+61) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	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 (a <= (-4.2d-11)) then
        tmp = x / a
    else if (a <= (-8.6d-161)) then
        tmp = x + ((-1.0d0) * (a * x))
    else if (a <= 4.5d+61) then
        tmp = z / b
    else
        tmp = x / a
    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 (a <= -4.2e-11) {
		tmp = x / a;
	} else if (a <= -8.6e-161) {
		tmp = x + (-1.0 * (a * x));
	} else if (a <= 4.5e+61) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4.2e-11:
		tmp = x / a
	elif a <= -8.6e-161:
		tmp = x + (-1.0 * (a * x))
	elif a <= 4.5e+61:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4.2e-11)
		tmp = Float64(x / a);
	elseif (a <= -8.6e-161)
		tmp = Float64(x + Float64(-1.0 * Float64(a * x)));
	elseif (a <= 4.5e+61)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -4.2e-11)
		tmp = x / a;
	elseif (a <= -8.6e-161)
		tmp = x + (-1.0 * (a * x));
	elseif (a <= 4.5e+61)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4.2e-11], N[(x / a), $MachinePrecision], If[LessEqual[a, -8.6e-161], N[(x + N[(-1.0 * N[(a * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e+61], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.1999999999999997e-11 or 4.5e61 < a

   1. Initial program 75.4%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 42.6%

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

   4. Applied rewrites 42.6%

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

   5. Taylor expanded in a around inf

      \[\leadsto \frac{x}{\color{blue}{a}} \]
   6. Step-by-step derivation

      1. lower-/.f64 26.1%

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

   7. Applied rewrites 26.1%

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

   if -4.1999999999999997e-11 < a < -8.5999999999999993e-161

   1. Initial program 75.4%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 42.6%

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

   4. Applied rewrites 42.6%

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

   5. Taylor expanded in a around 0

      \[\leadsto x + \color{blue}{-1 \cdot \left(a \cdot x\right)} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\left(a \cdot x\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \left(a \cdot \color{blue}{x}\right) \]

      3. lower-*.f64 19.4%

         \[\leadsto x + -1 \cdot \left(a \cdot x\right) \]

   7. Applied rewrites 19.4%

      \[\leadsto x + \color{blue}{-1 \cdot \left(a \cdot x\right)} \]

   if -8.5999999999999993e-161 < a < 4.5e61

   1. Initial program 75.4%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   3. Step-by-step derivation

      1. lower-/.f64 34.2%

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

   4. Applied rewrites 34.2%

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

Alternative 15: 42.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-161}:\\ \;\;\;\;\frac{x}{1}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+61}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (if (<= a -4.2e-11)
  (/ x a)
  (if (<= a -8.6e-161) (/ x 1.0) (if (<= a 4.5e+61) (/ z b) (/ x a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.2e-11) {
		tmp = x / a;
	} else if (a <= -8.6e-161) {
		tmp = x / 1.0;
	} else if (a <= 4.5e+61) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	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 (a <= (-4.2d-11)) then
        tmp = x / a
    else if (a <= (-8.6d-161)) then
        tmp = x / 1.0d0
    else if (a <= 4.5d+61) then
        tmp = z / b
    else
        tmp = x / a
    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 (a <= -4.2e-11) {
		tmp = x / a;
	} else if (a <= -8.6e-161) {
		tmp = x / 1.0;
	} else if (a <= 4.5e+61) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4.2e-11:
		tmp = x / a
	elif a <= -8.6e-161:
		tmp = x / 1.0
	elif a <= 4.5e+61:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4.2e-11)
		tmp = Float64(x / a);
	elseif (a <= -8.6e-161)
		tmp = Float64(x / 1.0);
	elseif (a <= 4.5e+61)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -4.2e-11)
		tmp = x / a;
	elseif (a <= -8.6e-161)
		tmp = x / 1.0;
	elseif (a <= 4.5e+61)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4.2e-11], N[(x / a), $MachinePrecision], If[LessEqual[a, -8.6e-161], N[(x / 1.0), $MachinePrecision], If[LessEqual[a, 4.5e+61], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.1999999999999997e-11 or 4.5e61 < a

   1. Initial program 75.4%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 42.6%

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

   4. Applied rewrites 42.6%

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

   5. Taylor expanded in a around inf

      \[\leadsto \frac{x}{\color{blue}{a}} \]
   6. Step-by-step derivation

      1. lower-/.f64 26.1%

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

   7. Applied rewrites 26.1%

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

   if -4.1999999999999997e-11 < a < -8.5999999999999993e-161

   1. Initial program 75.4%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 42.6%

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

   4. Applied rewrites 42.6%

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

   5. Taylor expanded in a around 0

      \[\leadsto \frac{x}{1} \]
   6. Step-by-step derivation

   7. Applied rewrites 19.8%

      \[\leadsto \frac{x}{1} \]

   if -8.5999999999999993e-161 < a < 4.5e61

   1. Initial program 75.4%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   3. Step-by-step derivation

      1. lower-/.f64 34.2%

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

   4. Applied rewrites 34.2%

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

Alternative 16: 41.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (if (<= a -4.2e-11) (/ x a) (if (<= a 6.2e-41) (/ x 1.0) (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.2e-11) {
		tmp = x / a;
	} else if (a <= 6.2e-41) {
		tmp = x / 1.0;
	} else {
		tmp = x / a;
	}
	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 (a <= (-4.2d-11)) then
        tmp = x / a
    else if (a <= 6.2d-41) then
        tmp = x / 1.0d0
    else
        tmp = x / a
    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 (a <= -4.2e-11) {
		tmp = x / a;
	} else if (a <= 6.2e-41) {
		tmp = x / 1.0;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4.2e-11:
		tmp = x / a
	elif a <= 6.2e-41:
		tmp = x / 1.0
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4.2e-11)
		tmp = Float64(x / a);
	elseif (a <= 6.2e-41)
		tmp = Float64(x / 1.0);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -4.2e-11)
		tmp = x / a;
	elseif (a <= 6.2e-41)
		tmp = x / 1.0;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4.2e-11], N[(x / a), $MachinePrecision], If[LessEqual[a, 6.2e-41], N[(x / 1.0), $MachinePrecision], N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -4.1999999999999997e-11 or 6.2e-41 < a

   1. Initial program 75.4%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 42.6%

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

   4. Applied rewrites 42.6%

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

   5. Taylor expanded in a around inf

      \[\leadsto \frac{x}{\color{blue}{a}} \]
   6. Step-by-step derivation

      1. lower-/.f64 26.1%

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

   7. Applied rewrites 26.1%

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

   if -4.1999999999999997e-11 < a < 6.2e-41

   1. Initial program 75.4%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-+.f64 42.6%

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

   4. Applied rewrites 42.6%

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

   5. Taylor expanded in a around 0

      \[\leadsto \frac{x}{1} \]
   6. Step-by-step derivation

   7. Applied rewrites 19.8%

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

Alternative 17: 26.1% accurate, 4.4× speedup

Math

\[\frac{x}{a} \]

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 75.4%

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

2. Taylor expanded in y around 0

   \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
3. Step-by-step derivation

   1. lower-/.f64 N/A

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

   2. lower-+.f64 42.6%

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

4. Applied rewrites 42.6%

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

5. Taylor expanded in a around inf

   \[\leadsto \frac{x}{\color{blue}{a}} \]
6. Step-by-step derivation

   1. lower-/.f64 26.1%

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

7. Applied rewrites 26.1%

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

Reproduce

herbie shell --seed 2025258 
(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))))