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

Percentage Accurate: 74.6% → 88.0%

Time: 7.0s

Alternatives: 13

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: 74.6% 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: 88.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+299}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+287}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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 -4e+299)
     (* (/ y (fma b y (fma a t t))) z)
     (if (<= t_1 2e+287) t_1 (/ 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 <= -4e+299) {
		tmp = (y / fma(b, y, fma(a, t, t))) * z;
	} else if (t_1 <= 2e+287) {
		tmp = t_1;
	} 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 <= -4e+299)
		tmp = Float64(Float64(y / fma(b, y, fma(a, t, t))) * z);
	elseif (t_1 <= 2e+287)
		tmp = t_1;
	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, -4e+299], N[(N[(y / N[(b * y + N[(a * t + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 2e+287], t$95$1, 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))) < -4.0000000000000002e299

   1. Initial program 17.0%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 82.4

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

   5. Applied rewrites 82.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 88.3%

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

   if -4.0000000000000002e299 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000002e287

   1. Initial program 90.8%

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

   if 2.0000000000000002e287 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.9%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 91.3

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

   5. Applied rewrites 91.3%

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

Alternative 2: 63.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + a}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_3 := \frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+296}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-305}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-307}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 a)))
        (t_2 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_3 (* (/ y (fma b y (fma a t t))) z)))
   (if (<= t_2 -2e+296)
     t_3
     (if (<= t_2 -2e-305)
       t_1
       (if (<= t_2 1e-307)
         t_3
         (if (<= t_2 4e+137) t_1 (if (<= t_2 INFINITY) t_3 (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + a);
	double t_2 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_3 = (y / fma(b, y, fma(a, t, t))) * z;
	double tmp;
	if (t_2 <= -2e+296) {
		tmp = t_3;
	} else if (t_2 <= -2e-305) {
		tmp = t_1;
	} else if (t_2 <= 1e-307) {
		tmp = t_3;
	} else if (t_2 <= 4e+137) {
		tmp = t_1;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + a))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_3 = Float64(Float64(y / fma(b, y, fma(a, t, t))) * z)
	tmp = 0.0
	if (t_2 <= -2e+296)
		tmp = t_3;
	elseif (t_2 <= -2e-305)
		tmp = t_1;
	elseif (t_2 <= 1e-307)
		tmp = t_3;
	elseif (t_2 <= 4e+137)
		tmp = t_1;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y / N[(b * y + N[(a * t + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+296], t$95$3, If[LessEqual[t$95$2, -2e-305], t$95$1, If[LessEqual[t$95$2, 1e-307], t$95$3, If[LessEqual[t$95$2, 4e+137], t$95$1, If[LessEqual[t$95$2, Infinity], t$95$3, 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))) < -1.99999999999999996e296 or -1.99999999999999999e-305 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.99999999999999909e-308 or 4.0000000000000001e137 < (/.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 52.9%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 66.6

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

   5. Applied rewrites 66.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 76.4%

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

   if -1.99999999999999996e296 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999999e-305 or 9.99999999999999909e-308 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 4.0000000000000001e137

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 53.6

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

   5. Applied rewrites 53.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 97.6

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

   5. Applied rewrites 97.6%

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

Alternative 3: 74.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_3 := \frac{t\_1}{1 + a}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+296}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-56}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\frac{y}{t}, b, 1 + a\right)}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+287}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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 (/ t_1 (+ 1.0 a))))
   (if (<= t_2 -2e+296)
     (* (/ y (fma b y (fma a t t))) z)
     (if (<= t_2 -1e-56)
       t_3
       (if (<= t_2 0.0)
         (/ x (fma (/ y t) b (+ 1.0 a)))
         (if (<= t_2 2e+287) t_3 (/ 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 = t_1 / (1.0 + a);
	double tmp;
	if (t_2 <= -2e+296) {
		tmp = (y / fma(b, y, fma(a, t, t))) * z;
	} else if (t_2 <= -1e-56) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = x / fma((y / t), b, (1.0 + a));
	} else if (t_2 <= 2e+287) {
		tmp = t_3;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_3 = Float64(t_1 / Float64(1.0 + a))
	tmp = 0.0
	if (t_2 <= -2e+296)
		tmp = Float64(Float64(y / fma(b, y, fma(a, t, t))) * z);
	elseif (t_2 <= -1e-56)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = Float64(x / fma(Float64(y / t), b, Float64(1.0 + a)));
	elseif (t_2 <= 2e+287)
		tmp = t_3;
	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[(t$95$1 / N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+296], N[(N[(y / N[(b * y + N[(a * t + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$2, -1e-56], t$95$3, If[LessEqual[t$95$2, 0.0], N[(x / N[(N[(y / t), $MachinePrecision] * b + N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+287], t$95$3, 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))) < -1.99999999999999996e296

   1. Initial program 21.5%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 83.3

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 88.8%

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

   if -1.99999999999999996e296 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1e-56 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000002e287

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-+.f64 78.0

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

   5. Applied rewrites 78.0%

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

   if -1e-56 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 76.1%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-+.f64 70.5

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

   5. Applied rewrites 70.5%

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

   if 2.0000000000000002e287 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.9%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 91.3

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

   5. Applied rewrites 91.3%

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

Alternative 4: 73.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := \frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{1 + a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+296}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-214}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\frac{y}{t}, b, 1 + a\right)}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+287}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2 (/ (fma (/ y t) z x) (+ 1.0 a))))
   (if (<= t_1 -2e+296)
     (* (/ y (fma b y (fma a t t))) z)
     (if (<= t_1 -1e-56)
       t_2
       (if (<= t_1 2e-214)
         (/ x (fma (/ y t) b (+ 1.0 a)))
         (if (<= t_1 2e+287) t_2 (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_2 = fma((y / t), z, x) / (1.0 + a);
	double tmp;
	if (t_1 <= -2e+296) {
		tmp = (y / fma(b, y, fma(a, t, t))) * z;
	} else if (t_1 <= -1e-56) {
		tmp = t_2;
	} else if (t_1 <= 2e-214) {
		tmp = x / fma((y / t), b, (1.0 + a));
	} else if (t_1 <= 2e+287) {
		tmp = t_2;
	} 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)))
	t_2 = Float64(fma(Float64(y / t), z, x) / Float64(1.0 + a))
	tmp = 0.0
	if (t_1 <= -2e+296)
		tmp = Float64(Float64(y / fma(b, y, fma(a, t, t))) * z);
	elseif (t_1 <= -1e-56)
		tmp = t_2;
	elseif (t_1 <= 2e-214)
		tmp = Float64(x / fma(Float64(y / t), b, Float64(1.0 + a)));
	elseif (t_1 <= 2e+287)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision] / N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+296], N[(N[(y / N[(b * y + N[(a * t + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, -1e-56], t$95$2, If[LessEqual[t$95$1, 2e-214], N[(x / N[(N[(y / t), $MachinePrecision] * b + N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+287], t$95$2, N[(z / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999996e296

   1. Initial program 21.5%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 83.3

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 88.8%

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

   if -1.99999999999999996e296 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1e-56 or 1.99999999999999983e-214 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000002e287

   1. Initial program 99.7%

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

   3. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*l/ N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 76.7

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

   5. Applied rewrites 76.7%

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

   if -1e-56 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.99999999999999983e-214

   1. Initial program 79.1%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-+.f64 71.6

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

   5. Applied rewrites 71.6%

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

   if 2.0000000000000002e287 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.9%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 91.3

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

   5. Applied rewrites 91.3%

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

Alternative 5: 60.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+296} \lor \neg \left(t\_1 \leq -2 \cdot 10^{-305} \lor \neg \left(t\_1 \leq 0 \lor \neg \left(t\_1 \leq 2 \cdot 10^{+287}\right)\right)\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (or (<= t_1 -2e+296)
           (not
            (or (<= t_1 -2e-305)
                (not (or (<= t_1 0.0) (not (<= t_1 2e+287)))))))
     (/ z b)
     (/ x (+ 1.0 a)))))

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 <= -2e+296) || !((t_1 <= -2e-305) || !((t_1 <= 0.0) || !(t_1 <= 2e+287)))) {
		tmp = z / b;
	} else {
		tmp = x / (1.0 + 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) :: t_1
    real(8) :: tmp
    t_1 = (x + ((y * z) / t)) / ((a + 1.0d0) + ((y * b) / t))
    if ((t_1 <= (-2d+296)) .or. (.not. (t_1 <= (-2d-305)) .or. (.not. (t_1 <= 0.0d0) .or. (.not. (t_1 <= 2d+287))))) then
        tmp = z / b
    else
        tmp = x / (1.0d0 + 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 t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if ((t_1 <= -2e+296) || !((t_1 <= -2e-305) || !((t_1 <= 0.0) || !(t_1 <= 2e+287)))) {
		tmp = z / b;
	} else {
		tmp = x / (1.0 + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if (t_1 <= -2e+296) or not ((t_1 <= -2e-305) or not ((t_1 <= 0.0) or not (t_1 <= 2e+287))):
		tmp = z / b
	else:
		tmp = x / (1.0 + a)
	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 <= -2e+296) || !((t_1 <= -2e-305) || !((t_1 <= 0.0) || !(t_1 <= 2e+287))))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(1.0 + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if ((t_1 <= -2e+296) || ~(((t_1 <= -2e-305) || ~(((t_1 <= 0.0) || ~((t_1 <= 2e+287)))))))
		tmp = z / b;
	else
		tmp = x / (1.0 + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+296], N[Not[Or[LessEqual[t$95$1, -2e-305], N[Not[Or[LessEqual[t$95$1, 0.0], N[Not[LessEqual[t$95$1, 2e+287]], $MachinePrecision]]], $MachinePrecision]]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(1.0 + a), $MachinePrecision]), $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))) < -1.99999999999999996e296 or -1.99999999999999999e-305 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 0.0 or 2.0000000000000002e287 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 28.2%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 74.1

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

   5. Applied rewrites 74.1%

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

   if -1.99999999999999996e296 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999999e-305 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000002e287

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 52.2

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

   5. Applied rewrites 52.2%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{+296} \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-305} \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0 \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+287}\right)\right)\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+296}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, t\right)} \cdot z\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-305} \lor \neg \left(t\_1 \leq 0 \lor \neg \left(t\_1 \leq 2 \cdot 10^{+287}\right)\right):\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 -2e+296)
     (* (/ y (fma b y t)) z)
     (if (or (<= t_1 -2e-305) (not (or (<= t_1 0.0) (not (<= t_1 2e+287)))))
       (/ x (+ 1.0 a))
       (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -2e+296) {
		tmp = (y / fma(b, y, t)) * z;
	} else if ((t_1 <= -2e-305) || !((t_1 <= 0.0) || !(t_1 <= 2e+287))) {
		tmp = x / (1.0 + a);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= -2e+296)
		tmp = Float64(Float64(y / fma(b, y, t)) * z);
	elseif ((t_1 <= -2e-305) || !((t_1 <= 0.0) || !(t_1 <= 2e+287)))
		tmp = Float64(x / 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, -2e+296], N[(N[(y / N[(b * y + t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[Or[LessEqual[t$95$1, -2e-305], N[Not[Or[LessEqual[t$95$1, 0.0], N[Not[LessEqual[t$95$1, 2e+287]], $MachinePrecision]]], $MachinePrecision]], N[(x / 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))) < -1.99999999999999996e296

   1. Initial program 21.5%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 83.3

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 67.0%

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

   if -1.99999999999999996e296 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999999e-305 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000002e287

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 52.2

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

   5. Applied rewrites 52.2%

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

   if -1.99999999999999999e-305 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 0.0 or 2.0000000000000002e287 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 29.5%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 79.4

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

   5. Applied rewrites 79.4%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{+296}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, t\right)} \cdot z\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-305} \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0 \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+287}\right)\right):\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+296}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+287}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{z}{t}, y, x\right)}{\mathsf{fma}\left(\frac{b}{t}, y, a - -1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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 -2e+296)
     (* (/ y (fma b y (fma a t t))) z)
     (if (<= t_1 2e+287)
       (/ (fma (/ z t) y x) (fma (/ b t) y (- a -1.0)))
       (/ 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 <= -2e+296) {
		tmp = (y / fma(b, y, fma(a, t, t))) * z;
	} else if (t_1 <= 2e+287) {
		tmp = fma((z / t), y, x) / fma((b / t), y, (a - -1.0));
	} 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 <= -2e+296)
		tmp = Float64(Float64(y / fma(b, y, fma(a, t, t))) * z);
	elseif (t_1 <= 2e+287)
		tmp = Float64(fma(Float64(z / t), y, x) / fma(Float64(b / t), y, Float64(a - -1.0)));
	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, -2e+296], N[(N[(y / N[(b * y + N[(a * t + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 2e+287], N[(N[(N[(z / t), $MachinePrecision] * y + x), $MachinePrecision] / N[(N[(b / t), $MachinePrecision] * y + N[(a - -1.0), $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))) < -1.99999999999999996e296

   1. Initial program 21.5%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 83.3

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 88.8%

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

   if -1.99999999999999996e296 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000002e287

   1. Initial program 90.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 85.0

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lift-/.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-/l* N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. lower-/.f64 86.6

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

      17. lift-+.f64 N/A

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

      18. metadata-eval N/A

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

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

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

      20. metadata-eval N/A

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

      21. metadata-eval N/A

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

      22. metadata-eval N/A

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

      23. lower--.f64 N/A

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

      24. metadata-eval 86.6

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

   4. Applied rewrites 86.6%

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

   if 2.0000000000000002e287 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.9%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 91.3

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

   5. Applied rewrites 91.3%

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

Alternative 8: 69.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+296}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+287}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\frac{y}{t}, b, 1 + a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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 -2e+296)
     (* (/ y (fma b y (fma a t t))) z)
     (if (<= t_1 2e+287) (/ x (fma (/ y t) b (+ 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 <= -2e+296) {
		tmp = (y / fma(b, y, fma(a, t, t))) * z;
	} else if (t_1 <= 2e+287) {
		tmp = x / fma((y / t), b, (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 <= -2e+296)
		tmp = Float64(Float64(y / fma(b, y, fma(a, t, t))) * z);
	elseif (t_1 <= 2e+287)
		tmp = Float64(x / fma(Float64(y / t), b, 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, -2e+296], N[(N[(y / N[(b * y + N[(a * t + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 2e+287], N[(x / N[(N[(y / t), $MachinePrecision] * b + 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))) < -1.99999999999999996e296

   1. Initial program 21.5%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 83.3

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 88.8%

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

   if -1.99999999999999996e296 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000002e287

   1. Initial program 90.8%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-+.f64 63.9

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

   5. Applied rewrites 63.9%

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

   if 2.0000000000000002e287 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.9%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 91.3

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

   5. Applied rewrites 91.3%

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

Alternative 9: 60.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+208}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-61}:\\ \;\;\;\;\frac{y}{t\_1} \cdot z\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-77}:\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+109}:\\ \;\;\;\;\frac{z \cdot y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma b y (fma a t t))))
   (if (<= y -1.8e+208)
     (/ z b)
     (if (<= y -6.5e-61)
       (* (/ y t_1) z)
       (if (<= y 4.8e-77)
         (/ x (+ 1.0 a))
         (if (<= y 2.6e+109) (/ (* z y) t_1) (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(b, y, fma(a, t, t));
	double tmp;
	if (y <= -1.8e+208) {
		tmp = z / b;
	} else if (y <= -6.5e-61) {
		tmp = (y / t_1) * z;
	} else if (y <= 4.8e-77) {
		tmp = x / (1.0 + a);
	} else if (y <= 2.6e+109) {
		tmp = (z * y) / t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(b, y, fma(a, t, t))
	tmp = 0.0
	if (y <= -1.8e+208)
		tmp = Float64(z / b);
	elseif (y <= -6.5e-61)
		tmp = Float64(Float64(y / t_1) * z);
	elseif (y <= 4.8e-77)
		tmp = Float64(x / Float64(1.0 + a));
	elseif (y <= 2.6e+109)
		tmp = Float64(Float64(z * y) / t_1);
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * y + N[(a * t + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+208], N[(z / b), $MachinePrecision], If[LessEqual[y, -6.5e-61], N[(N[(y / t$95$1), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[y, 4.8e-77], N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+109], N[(N[(z * y), $MachinePrecision] / t$95$1), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.80000000000000001e208 or 2.5999999999999998e109 < y

   1. Initial program 34.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 69.0

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

   5. Applied rewrites 69.0%

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

   if -1.80000000000000001e208 < y < -6.4999999999999994e-61

   1. Initial program 66.8%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 40.6

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

   5. Applied rewrites 40.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 56.2%

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

   if -6.4999999999999994e-61 < y < 4.7999999999999998e-77

   1. Initial program 94.3%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 67.2

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

   5. Applied rewrites 67.2%

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

   if 4.7999999999999998e-77 < y < 2.5999999999999998e109

   1. Initial program 89.1%

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

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 73.3

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

   5. Applied rewrites 73.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 76.2%

      \[\leadsto \frac{y}{\mathsf{fma}\left(b, y, \mathsf{fma}\left(a, t, t\right)\right)} \cdot z \]
   9. Step-by-step derivation

   10. Applied rewrites 78.8%

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

Alternative 10: 41.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a + 1 \leq -200 \lor \neg \left(a + 1 \leq 1.02\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ a 1.0) -200.0) (not (<= (+ a 1.0) 1.02)))
   (/ x a)
   (fma (- a) x x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a + 1.0) <= -200.0) || !((a + 1.0) <= 1.02)) {
		tmp = x / a;
	} else {
		tmp = fma(-a, x, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a + 1.0) <= -200.0) || !(Float64(a + 1.0) <= 1.02))
		tmp = Float64(x / a);
	else
		tmp = fma(Float64(-a), x, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a + 1.0), $MachinePrecision], -200.0], N[Not[LessEqual[N[(a + 1.0), $MachinePrecision], 1.02]], $MachinePrecision]], N[(x / a), $MachinePrecision], N[((-a) * x + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 a #s(literal 1 binary64)) < -200 or 1.02 < (+.f64 a #s(literal 1 binary64))

   1. Initial program 66.7%

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

   3. Taylor expanded in a around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*l/ N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 57.3

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

   5. Applied rewrites 57.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 41.5%

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

   if -200 < (+.f64 a #s(literal 1 binary64)) < 1.02

   1. Initial program 71.3%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 29.3

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

   5. Applied rewrites 29.3%

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

   6. Taylor expanded in a around 0

      \[\leadsto x + \color{blue}{-1 \cdot \left(a \cdot x\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 28.4%

      \[\leadsto \mathsf{fma}\left(-a, \color{blue}{x}, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -200 \lor \neg \left(a + 1 \leq 1.02\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -13 \lor \neg \left(t \leq 1.2 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -13.0) (not (<= t 1.2e-37))) (/ x a) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -13.0) || !(t <= 1.2e-37)) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-13.0d0)) .or. (.not. (t <= 1.2d-37))) then
        tmp = x / a
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -13.0) || !(t <= 1.2e-37)) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -13.0) or not (t <= 1.2e-37):
		tmp = x / a
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -13.0) || !(t <= 1.2e-37))
		tmp = Float64(x / a);
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -13.0) || ~((t <= 1.2e-37)))
		tmp = x / a;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -13.0], N[Not[LessEqual[t, 1.2e-37]], $MachinePrecision]], N[(x / a), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -13 or 1.19999999999999995e-37 < t

   1. Initial program 79.1%

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

   3. Taylor expanded in a around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*l/ N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 48.2

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

   5. Applied rewrites 48.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 38.1%

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

   if -13 < t < 1.19999999999999995e-37

   1. Initial program 60.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 59.7

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

   5. Applied rewrites 59.7%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -13 \lor \neg \left(t \leq 1.2 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 19.3% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(-a, x, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 69.0%

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

3. Taylor expanded in y around 0

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

   1. lower-/.f64 N/A

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

   2. lower-+.f64 35.8

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

5. Applied rewrites 35.8%

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

6. Taylor expanded in a around 0

   \[\leadsto x + \color{blue}{-1 \cdot \left(a \cdot x\right)} \]
7. Step-by-step derivation

8. Applied rewrites 15.2%

   \[\leadsto \mathsf{fma}\left(-a, \color{blue}{x}, x\right) \]
9. Add Preprocessing

Alternative 13: 4.1% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \left(-a\right) \cdot x \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return -a * 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 = -a * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.0%

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

3. Taylor expanded in y around 0

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

   1. lower-/.f64 N/A

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

   2. lower-+.f64 35.8

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

5. Applied rewrites 35.8%

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

6. Taylor expanded in a around 0

   \[\leadsto x + \color{blue}{-1 \cdot \left(a \cdot x\right)} \]
7. Step-by-step derivation

8. Applied rewrites 15.2%

   \[\leadsto \mathsf{fma}\left(-a, \color{blue}{x}, x\right) \]

9. Taylor expanded in a around inf

   \[\leadsto -1 \cdot \left(a \cdot \color{blue}{x}\right) \]
10. Step-by-step derivation

11. Applied rewrites 4.0%

    \[\leadsto \left(-a\right) \cdot x \]
12. Add Preprocessing

Developer Target 1: 79.3% 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 2025017 
(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))))