Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1

Percentage Accurate: 97.7% → 97.7%

Time: 3.5s

Alternatives: 11

Speedup: 1.0×

• 24.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (+ (* (/ x y) (- z t)) t))

C

double code(double x, double y, double z, double t) {
	return ((x / y) * (z - t)) + 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x / y) * (z - t)) + t
end function

Java

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

Python

def code(x, y, z, t):
	return ((x / y) * (z - t)) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x / y) * Float64(z - t)) + t)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (+ (* (/ x y) (- z t)) t))

C

double code(double x, double y, double z, double t) {
	return ((x / y) * (z - t)) + 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x / y) * (z - t)) + t
end function

Java

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

Python

def code(x, y, z, t):
	return ((x / y) * (z - t)) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x / y) * Float64(z - t)) + t)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

Alternative 1: 97.7% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (+ (* (/ x y) (- z t)) t))

C

double code(double x, double y, double z, double t) {
	return ((x / y) * (z - t)) + 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x / y) * (z - t)) + t
end function

Java

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

Python

def code(x, y, z, t):
	return ((x / y) * (z - t)) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x / y) * Float64(z - t)) + t)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

Derivation

1. Initial program 98.0%

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

Alternative 2: 75.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{y} \cdot t\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 500000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (- x) y) t)))
   (if (<= (/ x y) -5e+95)
     t_1
     (if (<= (/ x y) 500000000.0)
       (fma (/ x y) z t)
       (if (<= (/ x y) 2e+114) t_1 (/ (* x z) y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (-x / y) * t;
	double tmp;
	if ((x / y) <= -5e+95) {
		tmp = t_1;
	} else if ((x / y) <= 500000000.0) {
		tmp = fma((x / y), z, t);
	} else if ((x / y) <= 2e+114) {
		tmp = t_1;
	} else {
		tmp = (x * z) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(-x) / y) * t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+95)
		tmp = t_1;
	elseif (Float64(x / y) <= 500000000.0)
		tmp = fma(Float64(x / y), z, t);
	elseif (Float64(x / y) <= 2e+114)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * z) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[((-x) / y), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e+95], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 500000000.0], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e+114], t$95$1, N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5.00000000000000025e95 or 5e8 < (/.f64 x y) < 2e114

   1. Initial program 96.7%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-lft-identity N/A

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

      5. distribute-rgt-in N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

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

         \[\leadsto \left(1 - \left(\mathsf{neg}\left(-1\right)\right) \cdot \frac{x}{y}\right) \cdot t \]

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

      11. lower--.f64 N/A

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

      12. lift-/.f64 67.2

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

   5. Applied rewrites 67.2%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(-1 \cdot \frac{x}{y}\right) \cdot t \]
   7. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{-1 \cdot x}{y} \cdot t \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot x}{y} \cdot t \]

      3. mul-1-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(x\right)}{y} \cdot t \]

      4. lower-neg.f64 67.2

         \[\leadsto \frac{-x}{y} \cdot t \]

   8. Applied rewrites 67.2%

      \[\leadsto \frac{-x}{y} \cdot t \]

   if -5.00000000000000025e95 < (/.f64 x y) < 5e8

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 92.4%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-/.f64 92.4

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

   7. Applied rewrites 92.4%

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

   if 2e114 < (/.f64 x y)

   1. Initial program 98.0%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 69.7

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

   7. Applied rewrites 69.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 69.8

         \[\leadsto \frac{x \cdot z}{y} \]

   9. Applied rewrites 69.8%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+95}:\\ \;\;\;\;\frac{-x}{y} \cdot t\\ \mathbf{elif}\;\frac{x}{y} \leq 500000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+114}:\\ \;\;\;\;\frac{-x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \lor \neg \left(\frac{x}{y} \leq 4000000\right):\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{y} + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1.0) (not (<= (/ x y) 4000000.0)))
   (* (/ (- z t) y) x)
   (+ (/ (* x z) y) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.0) || !((x / y) <= 4000000.0)) {
		tmp = ((z - t) / y) * x;
	} else {
		tmp = ((x * z) / y) + t;
	}
	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)
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) :: tmp
    if (((x / y) <= (-1.0d0)) .or. (.not. ((x / y) <= 4000000.0d0))) then
        tmp = ((z - t) / y) * x
    else
        tmp = ((x * z) / y) + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.0) || !((x / y) <= 4000000.0)) {
		tmp = ((z - t) / y) * x;
	} else {
		tmp = ((x * z) / y) + t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1.0) or not ((x / y) <= 4000000.0):
		tmp = ((z - t) / y) * x
	else:
		tmp = ((x * z) / y) + t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1.0) || !(Float64(x / y) <= 4000000.0))
		tmp = Float64(Float64(Float64(z - t) / y) * x);
	else
		tmp = Float64(Float64(Float64(x * z) / y) + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1.0) || ~(((x / y) <= 4000000.0)))
		tmp = ((z - t) / y) * x;
	else
		tmp = ((x * z) / y) + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4000000.0]], $MachinePrecision]], N[(N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision] + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1 or 4e6 < (/.f64 x y)

   1. Initial program 97.7%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 96.3

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

   5. Applied rewrites 96.3%

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

   if -1 < (/.f64 x y) < 4e6

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 97.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 98.0

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

   7. Applied rewrites 98.0%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \lor \neg \left(\frac{x}{y} \leq 4000000\right):\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{y} + t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+24} \lor \neg \left(\frac{x}{y} \leq 4000000\right):\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+24) (not (<= (/ x y) 4000000.0)))
   (* (/ (- z t) y) x)
   (fma (/ x y) z t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+24) || !((x / y) <= 4000000.0)) {
		tmp = ((z - t) / y) * x;
	} else {
		tmp = fma((x / y), z, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e+24) || !(Float64(x / y) <= 4000000.0))
		tmp = Float64(Float64(Float64(z - t) / y) * x);
	else
		tmp = fma(Float64(x / y), z, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e+24], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4000000.0]], $MachinePrecision]], N[(N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.00000000000000045e24 or 4e6 < (/.f64 x y)

   1. Initial program 97.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 97.6

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

   5. Applied rewrites 97.6%

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

   if -5.00000000000000045e24 < (/.f64 x y) < 4e6

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 96.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-/.f64 96.0

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

   7. Applied rewrites 96.0%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+24} \lor \neg \left(\frac{x}{y} \leq 4000000\right):\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-23} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{z}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e-23) (not (<= (/ x y) 2e-33))) (* (/ z y) x) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e-23) || !((x / y) <= 2e-33)) {
		tmp = (z / y) * x;
	} else {
		tmp = t;
	}
	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)
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) :: tmp
    if (((x / y) <= (-1d-23)) .or. (.not. ((x / y) <= 2d-33))) then
        tmp = (z / y) * x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e-23) || !((x / y) <= 2e-33)) {
		tmp = (z / y) * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e-23) or not ((x / y) <= 2e-33):
		tmp = (z / y) * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e-23) || !(Float64(x / y) <= 2e-33))
		tmp = Float64(Float64(z / y) * x);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e-23) || ~(((x / y) <= 2e-33)))
		tmp = (z / y) * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e-23], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-33]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] * x), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.9999999999999996e-24 or 2.0000000000000001e-33 < (/.f64 x y)

   1. Initial program 97.8%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 54.6

         \[\leadsto \frac{z}{y} \cdot x \]

   5. Applied rewrites 54.6%

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

   if -9.9999999999999996e-24 < (/.f64 x y) < 2.0000000000000001e-33

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Applied rewrites 78.7%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-23} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{z}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-23}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-33}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1e-23)
   (/ (* x z) y)
   (if (<= (/ x y) 2e-33) t (* (/ z y) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1e-23) {
		tmp = (x * z) / y;
	} else if ((x / y) <= 2e-33) {
		tmp = t;
	} else {
		tmp = (z / y) * x;
	}
	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)
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) :: tmp
    if ((x / y) <= (-1d-23)) then
        tmp = (x * z) / y
    else if ((x / y) <= 2d-33) then
        tmp = t
    else
        tmp = (z / y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1e-23) {
		tmp = (x * z) / y;
	} else if ((x / y) <= 2e-33) {
		tmp = t;
	} else {
		tmp = (z / y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1e-23:
		tmp = (x * z) / y
	elif (x / y) <= 2e-33:
		tmp = t
	else:
		tmp = (z / y) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1e-23)
		tmp = Float64(Float64(x * z) / y);
	elseif (Float64(x / y) <= 2e-33)
		tmp = t;
	else
		tmp = Float64(Float64(z / y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1e-23)
		tmp = (x * z) / y;
	elseif ((x / y) <= 2e-33)
		tmp = t;
	else
		tmp = (z / y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1e-23], N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-33], t, N[(N[(z / y), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -9.9999999999999996e-24

   1. Initial program 97.1%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 97.1

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

   4. Applied rewrites 97.1%

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

   5. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 49.4

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

   7. Applied rewrites 49.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 54.5

         \[\leadsto \frac{x \cdot z}{y} \]

   9. Applied rewrites 54.5%

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

   if -9.9999999999999996e-24 < (/.f64 x y) < 2.0000000000000001e-33

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Applied rewrites 78.7%

      \[\leadsto \color{blue}{t} \]

   if 2.0000000000000001e-33 < (/.f64 x y)

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 59.5

         \[\leadsto \frac{z}{y} \cdot x \]

   5. Applied rewrites 59.5%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-23}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-33}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-35} \lor \neg \left(z \leq 2 \cdot 10^{-192}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.3e-35) (not (<= z 2e-192)))
   (fma (/ x y) z t)
   (* (- 1.0 (/ x y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.3e-35) || !(z <= 2e-192)) {
		tmp = fma((x / y), z, t);
	} else {
		tmp = (1.0 - (x / y)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.3e-35) || !(z <= 2e-192))
		tmp = fma(Float64(x / y), z, t);
	else
		tmp = Float64(Float64(1.0 - Float64(x / y)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.3e-35], N[Not[LessEqual[z, 2e-192]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3000000000000002e-35 or 2.0000000000000002e-192 < z

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 87.9%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-/.f64 87.9

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

   7. Applied rewrites 87.9%

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

   if -4.3000000000000002e-35 < z < 2.0000000000000002e-192

   1. Initial program 96.7%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-lft-identity N/A

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

      5. distribute-rgt-in N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

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

         \[\leadsto \left(1 - \left(\mathsf{neg}\left(-1\right)\right) \cdot \frac{x}{y}\right) \cdot t \]

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

      11. lower--.f64 N/A

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

      12. lift-/.f64 90.1

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

   5. Applied rewrites 90.1%

      \[\leadsto \color{blue}{\left(1 - \frac{x}{y}\right) \cdot t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-35} \lor \neg \left(z \leq 2 \cdot 10^{-192}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3.9 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{y}, x, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{y} + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 3.9e+111) (fma (/ (- z t) y) x t) (+ (/ (* x z) y) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 3.9e+111) {
		tmp = fma(((z - t) / y), x, t);
	} else {
		tmp = ((x * z) / y) + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 3.9e+111)
		tmp = fma(Float64(Float64(z - t) / y), x, t);
	else
		tmp = Float64(Float64(Float64(x * z) / y) + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 3.9e+111], N[(N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] * x + t), $MachinePrecision], N[(N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision] + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.89999999999999979e111

   1. Initial program 98.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*l/ N/A

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

      6. associate-/l* N/A

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

      7. sub-div N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-div N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 95.5

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

   4. Applied rewrites 95.5%

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

   if 3.89999999999999979e111 < z

   1. Initial program 97.2%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 97.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 99.7

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

   7. Applied rewrites 99.7%

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

Alternative 9: 77.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{x}{y}, z, t\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (fma (/ x y) z t))

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in z around inf

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

5. Applied rewrites 76.0%

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

   1. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. lower-fma.f64 N/A

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

   5. lift-/.f64 76.0

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

7. Applied rewrites 76.0%

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

Alternative 10: 73.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{z}{y}, x, t\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (fma (/ z y) x t))

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. lift-/.f64 N/A

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

   5. associate-*l/ N/A

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

   6. associate-/l* N/A

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

   7. sub-div N/A

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

   8. *-commutative N/A

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

   9. lower-fma.f64 N/A

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

   10. sub-div N/A

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

   11. lower-/.f64 N/A

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

   12. lift--.f64 94.2

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

4. Applied rewrites 94.2%

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

5. Taylor expanded in z around inf

   \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{z}{y}}, x, t\right) \]
6. Step-by-step derivation

   1. lift-/.f64 73.3

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

7. Applied rewrites 73.3%

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

Alternative 11: 38.6% accurate, 23.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{t} \]
4. Step-by-step derivation

5. Applied rewrites 35.7%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Developer Target 1: 97.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* (/ x y) (- z t)) t)))
   (if (< z 2.759456554562692e-282)
     t_1
     (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: tmp
    t_1 = ((x / y) * (z - t)) + t
    if (z < 2.759456554562692d-282) then
        tmp = t_1
    else if (z < 2.326994450874436d-110) then
        tmp = (x * ((z - t) / y)) + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x / y) * (z - t)) + t
	tmp = 0
	if z < 2.759456554562692e-282:
		tmp = t_1
	elif z < 2.326994450874436e-110:
		tmp = (x * ((z - t) / y)) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x / y) * Float64(z - t)) + t)
	tmp = 0.0
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = Float64(Float64(x * Float64(Float64(z - t) / y)) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x / y) * (z - t)) + t;
	tmp = 0.0;
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = (x * ((z - t) / y)) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]}, If[Less[z, 2.759456554562692e-282], t$95$1, If[Less[z, 2.326994450874436e-110], N[(N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2025064 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z 689864138640673/250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* (/ x y) (- z t)) t) (if (< z 581748612718609/25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t))))

  (+ (* (/ x y) (- z t)) t))