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

Percentage Accurate: 75.5% → 89.8%

Time: 5.1s

Alternatives: 12

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x + ((y * z) / t)) / ((a + 1.0d0) + ((y * b) / t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x + ((y * z) / t)) / ((a + 1.0d0) + ((y * b) / t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_3 := \mathsf{fma}\left(\frac{b}{t}, y, a + 1\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t\_3 \cdot t}, \frac{x}{t\_3}\right)\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-311}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\frac{t\_1}{\mathsf{fma}\left(y, \frac{b}{t}, 1 + a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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 (fma (/ b t) y (+ a 1.0))))
   (if (<= t_2 (- INFINITY))
     (fma y (/ z (* t_3 t)) (/ x t_3))
     (if (<= t_2 -5e-311)
       t_2
       (if (<= t_2 5e+301) (/ t_1 (fma y (/ b t) (+ 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);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double t_3 = fma((b / t), y, (a + 1.0));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = fma(y, (z / (t_3 * t)), (x / t_3));
	} else if (t_2 <= -5e-311) {
		tmp = t_2;
	} else if (t_2 <= 5e+301) {
		tmp = t_1 / fma(y, (b / t), (1.0 + a));
	} 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 = fma(Float64(b / t), y, Float64(a + 1.0))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = fma(y, Float64(z / Float64(t_3 * t)), Float64(x / t_3));
	elseif (t_2 <= -5e-311)
		tmp = t_2;
	elseif (t_2 <= 5e+301)
		tmp = Float64(t_1 / fma(y, Float64(b / t), Float64(1.0 + a)));
	else
		tmp = Float64(z / b);
	end
	return 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[(N[(b / t), $MachinePrecision] * y + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(y * N[(z / N[(t$95$3 * t), $MachinePrecision]), $MachinePrecision] + N[(x / t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-311], t$95$2, If[LessEqual[t$95$2, 5e+301], N[(t$95$1 / N[(y * N[(b / t), $MachinePrecision] + N[(1.0 + a), $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 30.9%

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

      1. lift-+.f64 N/A

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

      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. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-+.f64 30.8

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

   3. Applied rewrites 30.8%

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

   5. Applied rewrites 87.1%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -5.00000000000023e-311

   1. Initial program 99.3%

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

   if -5.00000000000023e-311 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5.0000000000000004e301

   1. Initial program 84.8%

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

      1. lift-+.f64 N/A

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

      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. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-+.f64 86.1

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

   3. Applied rewrites 86.1%

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

   if 5.0000000000000004e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 12.9%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 82.1

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

   4. Applied rewrites 82.1%

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

Alternative 2: 89.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\mathsf{fma}\left(\frac{b}{t}, y, a + 1\right)}\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-311}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\frac{t\_1}{\mathsf{fma}\left(y, \frac{b}{t}, 1 + a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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))
     (* (/ y t) (/ z (fma (/ b t) y (+ a 1.0))))
     (if (<= t_2 -5e-311)
       t_2
       (if (<= t_2 5e+301) (/ t_1 (fma y (/ b t) (+ 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);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (y / t) * (z / fma((b / t), y, (a + 1.0)));
	} else if (t_2 <= -5e-311) {
		tmp = t_2;
	} else if (t_2 <= 5e+301) {
		tmp = t_1 / fma(y, (b / t), (1.0 + a));
	} 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(Float64(y / t) * Float64(z / fma(Float64(b / t), y, Float64(a + 1.0))));
	elseif (t_2 <= -5e-311)
		tmp = t_2;
	elseif (t_2 <= 5e+301)
		tmp = Float64(t_1 / fma(y, Float64(b / t), Float64(1.0 + a)));
	else
		tmp = Float64(z / b);
	end
	return 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[(N[(y / t), $MachinePrecision] * N[(z / N[(N[(b / t), $MachinePrecision] * y + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-311], t$95$2, If[LessEqual[t$95$2, 5e+301], N[(t$95$1 / N[(y * N[(b / t), $MachinePrecision] + N[(1.0 + a), $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 30.9%

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

      1. lift-+.f64 N/A

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

      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. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-+.f64 30.8

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

   3. Applied rewrites 30.8%

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

   4. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. associate-+r+ N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. associate-*r/ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift-/.f64 N/A

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

      15. +-commutative N/A

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

      16. lift-+.f64 80.4

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

   6. Applied rewrites 80.4%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -5.00000000000023e-311

   1. Initial program 99.3%

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

   if -5.00000000000023e-311 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5.0000000000000004e301

   1. Initial program 84.8%

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

      1. lift-+.f64 N/A

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

      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. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-+.f64 86.1

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

   3. Applied rewrites 86.1%

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

   if 5.0000000000000004e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 12.9%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 82.1

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

   4. Applied rewrites 82.1%

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

Alternative 3: 72.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\mathsf{fma}\left(\frac{b}{t}, y, a + 1\right)}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-309}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(b, \frac{y}{t}, 1 + a\right)}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\frac{t\_1}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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))
     (* (/ y t) (/ z (fma (/ b t) y (+ a 1.0))))
     (if (<= t_2 5e-309)
       (/ x (fma b (/ y t) (+ 1.0 a)))
       (if (<= t_2 5e+301) (/ t_1 (+ 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);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (y / t) * (z / fma((b / t), y, (a + 1.0)));
	} else if (t_2 <= 5e-309) {
		tmp = x / fma(b, (y / t), (1.0 + a));
	} else if (t_2 <= 5e+301) {
		tmp = t_1 / (1.0 + a);
	} 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(Float64(y / t) * Float64(z / fma(Float64(b / t), y, Float64(a + 1.0))));
	elseif (t_2 <= 5e-309)
		tmp = Float64(x / fma(b, Float64(y / t), Float64(1.0 + a)));
	elseif (t_2 <= 5e+301)
		tmp = Float64(t_1 / Float64(1.0 + a));
	else
		tmp = Float64(z / b);
	end
	return 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[(N[(y / t), $MachinePrecision] * N[(z / N[(N[(b / t), $MachinePrecision] * y + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e-309], N[(x / N[(b * N[(y / t), $MachinePrecision] + N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+301], N[(t$95$1 / N[(1.0 + a), $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 30.9%

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

      1. lift-+.f64 N/A

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

      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. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-+.f64 30.8

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

   3. Applied rewrites 30.8%

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

   4. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. associate-+r+ N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. associate-*r/ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift-/.f64 N/A

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

      15. +-commutative N/A

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

      16. lift-+.f64 80.4

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

   6. Applied rewrites 80.4%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 4.9999999999999995e-309

   1. Initial program 85.4%

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

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. associate-+r+ N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 65.6

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

   4. Applied rewrites 65.6%

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

   if 4.9999999999999995e-309 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5.0000000000000004e301

   1. Initial program 99.1%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 76.1

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

   4. Applied rewrites 76.1%

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

   if 5.0000000000000004e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 12.9%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 82.1

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

   4. Applied rewrites 82.1%

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

Alternative 4: 70.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-309}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(b, \frac{y}{t}, 1 + a\right)}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\frac{t\_1}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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 b)
     (if (<= t_2 5e-309)
       (/ x (fma b (/ y t) (+ 1.0 a)))
       (if (<= t_2 5e+301) (/ t_1 (+ 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);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z / b;
	} else if (t_2 <= 5e-309) {
		tmp = x / fma(b, (y / t), (1.0 + a));
	} else if (t_2 <= 5e+301) {
		tmp = t_1 / (1.0 + a);
	} 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 / b);
	elseif (t_2 <= 5e-309)
		tmp = Float64(x / fma(b, Float64(y / t), Float64(1.0 + a)));
	elseif (t_2 <= 5e+301)
		tmp = Float64(t_1 / Float64(1.0 + a));
	else
		tmp = Float64(z / b);
	end
	return 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 / b), $MachinePrecision], If[LessEqual[t$95$2, 5e-309], N[(x / N[(b * N[(y / t), $MachinePrecision] + N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+301], N[(t$95$1 / N[(1.0 + a), $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 or 5.0000000000000004e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 17.7%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 74.8

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

   4. Applied rewrites 74.8%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 4.9999999999999995e-309

   1. Initial program 85.4%

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

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. associate-+r+ N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 65.6

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

   4. Applied rewrites 65.6%

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

   if 4.9999999999999995e-309 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5.0000000000000004e301

   1. Initial program 99.1%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 76.1

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

   4. Applied rewrites 76.1%

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

Alternative 5: 88.0% accurate, 0.3× speedup

Math

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

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))
     (* (/ y t) (/ z (fma (/ b t) y (+ a 1.0))))
     (if (<= t_2 5e+301) (/ t_1 (fma y (/ b t) (+ 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);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (y / t) * (z / fma((b / t), y, (a + 1.0)));
	} else if (t_2 <= 5e+301) {
		tmp = t_1 / fma(y, (b / t), (1.0 + a));
	} 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(Float64(y / t) * Float64(z / fma(Float64(b / t), y, Float64(a + 1.0))));
	elseif (t_2 <= 5e+301)
		tmp = Float64(t_1 / fma(y, Float64(b / t), Float64(1.0 + a)));
	else
		tmp = Float64(z / b);
	end
	return 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[(N[(y / t), $MachinePrecision] * N[(z / N[(N[(b / t), $MachinePrecision] * y + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+301], N[(t$95$1 / N[(y * N[(b / t), $MachinePrecision] + N[(1.0 + a), $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 30.9%

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

      1. lift-+.f64 N/A

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

      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. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-+.f64 30.8

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

   3. Applied rewrites 30.8%

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

   4. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. associate-+r+ N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. associate-*r/ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift-/.f64 N/A

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

      15. +-commutative N/A

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

      16. lift-+.f64 80.4

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

   6. Applied rewrites 80.4%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5.0000000000000004e301

   1. Initial program 90.7%

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

      1. lift-+.f64 N/A

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

      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. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-+.f64 89.6

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

   3. Applied rewrites 89.6%

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

   if 5.0000000000000004e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 12.9%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 82.1

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

   4. Applied rewrites 82.1%

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

Alternative 6: 67.4% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 (- INFINITY))
     (/ z b)
     (if (<= t_1 1e+297) (/ x (fma b (/ y t) (+ 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 <= 1e+297) {
		tmp = x / fma(b, (y / t), (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 <= 1e+297)
		tmp = Float64(x / fma(b, Float64(y / t), Float64(1.0 + a)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z / b), $MachinePrecision], If[LessEqual[t$95$1, 1e+297], N[(x / N[(b * N[(y / t), $MachinePrecision] + N[(1.0 + a), $MachinePrecision]), $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 1e297 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 18.2%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 74.4

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

   4. Applied rewrites 74.4%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1e297

   1. Initial program 90.7%

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

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. associate-+r+ N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 65.5

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

   4. Applied rewrites 65.5%

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

Alternative 7: 67.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-154}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \frac{z}{t}, x\right)}{1 + a}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-82}:\\ \;\;\;\;\frac{z + \frac{t \cdot x}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(b, \frac{y}{t}, 1 + a\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.3e-154)
   (/ (fma y (/ z t) x) (+ 1.0 a))
   (if (<= t 1.85e-82)
     (/ (+ z (/ (* t x) y)) b)
     (/ x (fma b (/ y t) (+ 1.0 a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.3e-154) {
		tmp = fma(y, (z / t), x) / (1.0 + a);
	} else if (t <= 1.85e-82) {
		tmp = (z + ((t * x) / y)) / b;
	} else {
		tmp = x / fma(b, (y / t), (1.0 + a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.3e-154)
		tmp = Float64(fma(y, Float64(z / t), x) / Float64(1.0 + a));
	elseif (t <= 1.85e-82)
		tmp = Float64(Float64(z + Float64(Float64(t * x) / y)) / b);
	else
		tmp = Float64(x / fma(b, Float64(y / t), Float64(1.0 + a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.3e-154], N[(N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision] / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e-82], N[(N[(z + N[(N[(t * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(x / N[(b * N[(y / t), $MachinePrecision] + N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3e-154

   1. Initial program 81.1%

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

   2. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 67.2

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

   4. Applied rewrites 67.2%

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

   if -2.3e-154 < t < 1.85e-82

   1. Initial program 60.9%

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

      1. lift-+.f64 N/A

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

      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. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-+.f64 52.5

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

   3. Applied rewrites 52.5%

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

   5. Applied rewrites 58.8%

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

   6. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 68.9

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

   8. Applied rewrites 68.9%

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

   if 1.85e-82 < t

   1. Initial program 82.8%

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

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. associate-+r+ N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 65.8

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

   4. Applied rewrites 65.8%

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

Alternative 8: 60.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + a}\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-57}:\\ \;\;\;\;\frac{z + \frac{t \cdot x}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 a))))
   (if (<= t -4.1e-42) t_1 (if (<= t 7.8e-57) (/ (+ z (/ (* t x) y)) 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 <= -4.1e-42) {
		tmp = t_1;
	} else if (t <= 7.8e-57) {
		tmp = (z + ((t * x) / y)) / 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 <= (-4.1d-42)) then
        tmp = t_1
    else if (t <= 7.8d-57) then
        tmp = (z + ((t * x) / y)) / 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 <= -4.1e-42) {
		tmp = t_1;
	} else if (t <= 7.8e-57) {
		tmp = (z + ((t * x) / y)) / 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 <= -4.1e-42:
		tmp = t_1
	elif t <= 7.8e-57:
		tmp = (z + ((t * x) / y)) / 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 <= -4.1e-42)
		tmp = t_1;
	elseif (t <= 7.8e-57)
		tmp = Float64(Float64(z + Float64(Float64(t * x) / y)) / 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 <= -4.1e-42)
		tmp = t_1;
	elseif (t <= 7.8e-57)
		tmp = (z + ((t * x) / y)) / 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, -4.1e-42], t$95$1, If[LessEqual[t, 7.8e-57], N[(N[(z + N[(N[(t * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.1000000000000001e-42 or 7.80000000000000013e-57 < t

   1. Initial program 82.7%

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

   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 57.6

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

   4. Applied rewrites 57.6%

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

   if -4.1000000000000001e-42 < t < 7.80000000000000013e-57

   1. Initial program 65.5%

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

      1. lift-+.f64 N/A

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

      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. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-+.f64 58.5

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

   3. Applied rewrites 58.5%

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

   5. Applied rewrites 64.0%

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

   6. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 64.3

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

   8. Applied rewrites 64.3%

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

Alternative 9: 56.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + a}\\ \mathbf{if}\;t \leq -2 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-57}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 a))))
   (if (<= t -2e-71) t_1 (if (<= t 1.9e-57) (/ 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 <= -2e-71) {
		tmp = t_1;
	} else if (t <= 1.9e-57) {
		tmp = 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 <= (-2d-71)) then
        tmp = t_1
    else if (t <= 1.9d-57) then
        tmp = 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 <= -2e-71) {
		tmp = t_1;
	} else if (t <= 1.9e-57) {
		tmp = 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 <= -2e-71:
		tmp = t_1
	elif t <= 1.9e-57:
		tmp = 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 <= -2e-71)
		tmp = t_1;
	elseif (t <= 1.9e-57)
		tmp = Float64(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 <= -2e-71)
		tmp = t_1;
	elseif (t <= 1.9e-57)
		tmp = 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, -2e-71], t$95$1, If[LessEqual[t, 1.9e-57], N[(z / b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9999999999999998e-71 or 1.8999999999999999e-57 < t

   1. Initial program 82.7%

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

   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 56.6

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

   4. Applied rewrites 56.6%

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

   if -1.9999999999999998e-71 < t < 1.8999999999999999e-57

   1. Initial program 64.4%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 55.2

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

   4. Applied rewrites 55.2%

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

Alternative 10: 42.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+38}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9e+17) (/ x a) (if (<= t 4.8e+38) (/ z b) (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9e+17) {
		tmp = x / a;
	} else if (t <= 4.8e+38) {
		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 (t <= (-9d+17)) then
        tmp = x / a
    else if (t <= 4.8d+38) 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 (t <= -9e+17) {
		tmp = x / a;
	} else if (t <= 4.8e+38) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9e+17:
		tmp = x / a
	elif t <= 4.8e+38:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9e+17)
		tmp = Float64(x / a);
	elseif (t <= 4.8e+38)
		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 (t <= -9e+17)
		tmp = x / a;
	elseif (t <= 4.8e+38)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9e+17], N[(x / a), $MachinePrecision], If[LessEqual[t, 4.8e+38], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -9e17 or 4.80000000000000035e38 < t

   1. Initial program 82.4%

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

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. associate-+r+ N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 70.9

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

   4. Applied rewrites 70.9%

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

   5. Taylor expanded in a around inf

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

      1. lower-/.f64 35.7

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

   7. Applied rewrites 35.7%

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

   if -9e17 < t < 4.80000000000000035e38

   1. Initial program 69.7%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 49.0

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

   4. Applied rewrites 49.0%

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

Alternative 11: 41.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.0) (/ x a) (if (<= a 1.05e-7) x (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.0) {
		tmp = x / a;
	} else if (a <= 1.05e-7) {
		tmp = x;
	} 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 <= (-1.0d0)) then
        tmp = x / a
    else if (a <= 1.05d-7) then
        tmp = x
    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 <= -1.0) {
		tmp = x / a;
	} else if (a <= 1.05e-7) {
		tmp = x;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.0:
		tmp = x / a
	elif a <= 1.05e-7:
		tmp = x
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.0)
		tmp = Float64(x / a);
	elseif (a <= 1.05e-7)
		tmp = x;
	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 <= -1.0)
		tmp = x / a;
	elseif (a <= 1.05e-7)
		tmp = x;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.0], N[(x / a), $MachinePrecision], If[LessEqual[a, 1.05e-7], x, N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1 or 1.05e-7 < a

   1. Initial program 74.7%

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

   2. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. associate-+r+ N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 54.2

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

   4. Applied rewrites 54.2%

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

   5. Taylor expanded in a around inf

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

      1. lower-/.f64 46.9

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

   7. Applied rewrites 46.9%

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

   if -1 < a < 1.05e-7

   1. Initial program 76.4%

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

   2. Taylor expanded in a around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 75.5

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

   4. Applied rewrites 75.5%

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

   5. Taylor expanded in y around 0

      \[\leadsto x \]
   6. Step-by-step derivation

   7. Applied rewrites 35.3%

      \[\leadsto x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 19.4% accurate, 53.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 75.5%

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

2. Taylor expanded in a around 0

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

   1. lower-/.f64 N/A

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

   2. +-commutative N/A

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

   3. associate-/l* N/A

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

   4. lower-fma.f64 N/A

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

   5. lower-/.f64 N/A

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

   6. +-commutative N/A

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

   7. associate-/l* N/A

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

   8. lower-fma.f64 N/A

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

   9. lower-/.f64 45.1

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

4. Applied rewrites 45.1%

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

5. Taylor expanded in y around 0

   \[\leadsto x \]
6. Step-by-step derivation

7. Applied rewrites 19.4%

   \[\leadsto x \]
8. Add Preprocessing

Developer Target 1: 80.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{if}\;t < -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.036967103737246 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))
   (if (< t -1.3659085366310088e-271)
     t_1
     (if (< t 3.036967103737246e-130) (/ z b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = 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 = 1.0d0 * ((x + ((y / t) * z)) * (1.0d0 / ((a + 1.0d0) + ((y / t) * b))))
    if (t < (-1.3659085366310088d-271)) then
        tmp = t_1
    else if (t < 3.036967103737246d-130) then
        tmp = 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 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))))
	tmp = 0
	if t < -1.3659085366310088e-271:
		tmp = t_1
	elif t < 3.036967103737246e-130:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 * Float64(Float64(x + Float64(Float64(y / t) * z)) * Float64(1.0 / Float64(Float64(a + 1.0) + Float64(Float64(y / t) * b)))))
	tmp = 0.0
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	tmp = 0.0;
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 * N[(N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.3659085366310088e-271], t$95$1, If[Less[t, 3.036967103737246e-130], N[(z / b), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2025106 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1707385670788761/12500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* 1 (* (+ x (* (/ y t) z)) (/ 1 (+ (+ a 1) (* (/ y t) b))))) (if (< t 1518483551868623/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ z b) (* 1 (* (+ x (* (/ y t) z)) (/ 1 (+ (+ a 1) (* (/ y t) b))))))))

  (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))