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

Percentage Accurate: 97.5% → 97.6%

Time: 2.7s

Alternatives: 9

Speedup: 1.1×

• 24.2% 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: 97.5% 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: 97.6% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.5%

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

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

   3. lift-/.f64 N/A

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

   4. lift--.f64 N/A

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

   5. lower-fma.f64 N/A

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

   6. lift-/.f64 N/A

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

   7. lift--.f64 97.6

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

3. Applied rewrites 97.6%

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

Alternative 2: 96.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{if}\;\frac{x}{y} \leq -1000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 0.04:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) (- z t))))
   (if (<= (/ x y) -1000.0) t_1 (if (<= (/ x y) 0.04) (fma (/ x y) z t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * (z - t);
	double tmp;
	if ((x / y) <= -1000.0) {
		tmp = t_1;
	} else if ((x / y) <= 0.04) {
		tmp = fma((x / y), z, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * Float64(z - t))
	tmp = 0.0
	if (Float64(x / y) <= -1000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 0.04)
		tmp = fma(Float64(x / y), z, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 0.04], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e3 or 0.0400000000000000008 < (/.f64 x y)

   1. Initial program 96.7%

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

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

      3. lift--.f64 N/A

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

      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 93.3

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

   3. Applied rewrites 93.3%

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

   4. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. sub-div N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 91.8

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

   6. Applied rewrites 91.8%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*l/ N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 95.5

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

   8. Applied rewrites 95.5%

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

   if -1e3 < (/.f64 x y) < 0.0400000000000000008

   1. Initial program 98.3%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 97.4%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{z} + t \]
   5. 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 97.4

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

   6. Applied rewrites 97.4%

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

Alternative 3: 94.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{y} \cdot x\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 0.04:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (- z t) y) x)))
   (if (<= (/ x y) -1e+38) t_1 (if (<= (/ x y) 0.04) (fma (/ x y) z t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((z - t) / y) * x;
	double tmp;
	if ((x / y) <= -1e+38) {
		tmp = t_1;
	} else if ((x / y) <= 0.04) {
		tmp = fma((x / y), z, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(z - t) / y) * x)
	tmp = 0.0
	if (Float64(x / y) <= -1e+38)
		tmp = t_1;
	elseif (Float64(x / y) <= 0.04)
		tmp = fma(Float64(x / y), z, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e+38], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 0.04], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.99999999999999977e37 or 0.0400000000000000008 < (/.f64 x y)

   1. Initial program 96.6%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{z}{y} - \frac{t}{y}\right)} \]
   3. 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 92.9

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

   4. Applied rewrites 92.9%

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

   if -9.99999999999999977e37 < (/.f64 x y) < 0.0400000000000000008

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 95.3%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{z} + t \]
   5. 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 95.3

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

   6. Applied rewrites 95.3%

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

Alternative 4: 85.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-33}:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (/ x y) z t)))
   (if (<= z -2.5e+44) t_1 (if (<= z 2.8e-33) (* (- 1.0 (/ x y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((x / y), z, t);
	double tmp;
	if (z <= -2.5e+44) {
		tmp = t_1;
	} else if (z <= 2.8e-33) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(x / y), z, t)
	tmp = 0.0
	if (z <= -2.5e+44)
		tmp = t_1;
	elseif (z <= 2.8e-33)
		tmp = Float64(Float64(1.0 - Float64(x / y)) * t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision]}, If[LessEqual[z, -2.5e+44], t$95$1, If[LessEqual[z, 2.8e-33], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4999999999999998e44 or 2.8e-33 < z

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 88.9%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{z} + t \]
   5. 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 88.9

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

   6. Applied rewrites 88.9%

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

   if -2.4999999999999998e44 < z < 2.8e-33

   1. Initial program 97.0%

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

   2. Taylor expanded in z around 0

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

      1. *-lft-identity N/A

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

      2. *-commutative N/A

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

      3. associate-*l/ N/A

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

      4. associate-*l* N/A

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

      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 82.9

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

   4. Applied rewrites 82.9%

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

Alternative 5: 77.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{y} \cdot t\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (- x) y) t)))
   (if (<= (/ x y) -1e+88)
     t_1
     (if (<= (/ x y) 10000000.0) (fma (/ x y) z t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (-x / y) * t;
	double tmp;
	if ((x / y) <= -1e+88) {
		tmp = t_1;
	} else if ((x / y) <= 10000000.0) {
		tmp = fma((x / y), z, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(-x) / y) * t)
	tmp = 0.0
	if (Float64(x / y) <= -1e+88)
		tmp = t_1;
	elseif (Float64(x / y) <= 10000000.0)
		tmp = fma(Float64(x / y), z, t);
	else
		tmp = t_1;
	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], -1e+88], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 10000000.0], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.99999999999999959e87 or 1e7 < (/.f64 x y)

   1. Initial program 96.3%

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

   2. Taylor expanded in z around 0

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

      1. *-lft-identity N/A

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

      2. *-commutative N/A

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

      3. associate-*l/ N/A

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

      4. associate-*l* N/A

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

      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 55.9

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

   4. Applied rewrites 55.9%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lift-neg.f64 N/A

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

      4. lower-/.f64 55.8

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

   7. Applied rewrites 55.8%

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

   if -9.99999999999999959e87 < (/.f64 x y) < 1e7

   1. Initial program 98.5%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 92.5%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{z} + t \]
   5. 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 92.5

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

   6. Applied rewrites 92.5%

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

Alternative 6: 64.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{y} \cdot t\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 500:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (- x) y) t)))
   (if (<= (/ x y) -1e+21) t_1 (if (<= (/ x y) 500.0) t t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (-x / y) * t;
	double tmp;
	if ((x / y) <= -1e+21) {
		tmp = t_1;
	} else if ((x / y) <= 500.0) {
		tmp = 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) * t
    if ((x / y) <= (-1d+21)) then
        tmp = t_1
    else if ((x / y) <= 500.0d0) then
        tmp = 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) * t;
	double tmp;
	if ((x / y) <= -1e+21) {
		tmp = t_1;
	} else if ((x / y) <= 500.0) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (-x / y) * t
	tmp = 0
	if (x / y) <= -1e+21:
		tmp = t_1
	elif (x / y) <= 500.0:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(-x) / y) * t)
	tmp = 0.0
	if (Float64(x / y) <= -1e+21)
		tmp = t_1;
	elseif (Float64(x / y) <= 500.0)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (-x / y) * t;
	tmp = 0.0;
	if ((x / y) <= -1e+21)
		tmp = t_1;
	elseif ((x / y) <= 500.0)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = 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], -1e+21], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 500.0], t, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e21 or 500 < (/.f64 x y)

   1. Initial program 96.6%

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

   2. Taylor expanded in z around 0

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

      1. *-lft-identity N/A

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

      2. *-commutative N/A

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

      3. associate-*l/ N/A

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

      4. associate-*l* N/A

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

      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 54.9

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

   4. Applied rewrites 54.9%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lift-neg.f64 N/A

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

      4. lower-/.f64 54.5

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

   7. Applied rewrites 54.5%

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

   if -1e21 < (/.f64 x y) < 500

   1. Initial program 98.4%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 73.0%

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

Alternative 7: 64.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-6}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-16}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e-6) (/ (* x z) y) (if (<= (/ x y) 1e-16) t (* (/ z y) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e-6) {
		tmp = (x * z) / y;
	} else if ((x / y) <= 1e-16) {
		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) <= (-2d-6)) then
        tmp = (x * z) / y
    else if ((x / y) <= 1d-16) 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) <= -2e-6) {
		tmp = (x * z) / y;
	} else if ((x / y) <= 1e-16) {
		tmp = t;
	} else {
		tmp = (z / y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e-6:
		tmp = (x * z) / y
	elif (x / y) <= 1e-16:
		tmp = t
	else:
		tmp = (z / y) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e-6)
		tmp = Float64(Float64(x * z) / y);
	elseif (Float64(x / y) <= 1e-16)
		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) <= -2e-6)
		tmp = (x * z) / y;
	elseif ((x / y) <= 1e-16)
		tmp = t;
	else
		tmp = (z / y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e-6], N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-16], t, N[(N[(z / y), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.99999999999999991e-6

   1. Initial program 96.5%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{x \cdot z}{y}} \]
   3. 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 51.9

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

   4. Applied rewrites 51.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 51.8

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

   6. Applied rewrites 51.8%

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

   if -1.99999999999999991e-6 < (/.f64 x y) < 9.9999999999999998e-17

   1. Initial program 98.3%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 77.2%

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

   if 9.9999999999999998e-17 < (/.f64 x y)

   1. Initial program 97.2%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{x \cdot z}{y}} \]
   3. 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 52.0

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

   4. Applied rewrites 52.0%

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

Alternative 8: 64.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{y} \cdot x\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-16}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z y) x)))
   (if (<= (/ x y) -2e-6) t_1 (if (<= (/ x y) 1e-16) t t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / y) * x;
	double tmp;
	if ((x / y) <= -2e-6) {
		tmp = t_1;
	} else if ((x / y) <= 1e-16) {
		tmp = 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 = (z / y) * x
    if ((x / y) <= (-2d-6)) then
        tmp = t_1
    else if ((x / y) <= 1d-16) then
        tmp = 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 = (z / y) * x;
	double tmp;
	if ((x / y) <= -2e-6) {
		tmp = t_1;
	} else if ((x / y) <= 1e-16) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / y) * x
	tmp = 0
	if (x / y) <= -2e-6:
		tmp = t_1
	elif (x / y) <= 1e-16:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / y) * x)
	tmp = 0.0
	if (Float64(x / y) <= -2e-6)
		tmp = t_1;
	elseif (Float64(x / y) <= 1e-16)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / y) * x;
	tmp = 0.0;
	if ((x / y) <= -2e-6)
		tmp = t_1;
	elseif ((x / y) <= 1e-16)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e-6], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1e-16], t, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.99999999999999991e-6 or 9.9999999999999998e-17 < (/.f64 x y)

   1. Initial program 96.8%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{x \cdot z}{y}} \]
   3. 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 51.9

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

   4. Applied rewrites 51.9%

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

   if -1.99999999999999991e-6 < (/.f64 x y) < 9.9999999999999998e-17

   1. Initial program 98.3%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 77.2%

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

Alternative 9: 40.0% accurate, 12.7× 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 97.5%

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

2. Taylor expanded in x around 0

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

4. Applied rewrites 40.0%

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

Reproduce

herbie shell --seed 2025115 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64
  (+ (* (/ x y) (- z t)) t))