Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.7s

Alternatives: 10

Speedup: 1.0×

• 34.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 2: 59.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+165}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-159}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-13}:\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+191}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= z -1.15e+165)
     (* z x)
     (if (<= z -2.85e-21)
       t_1
       (if (<= z 3.8e-159)
         (fma t y x)
         (if (<= z 6e-13) (* (- t x) y) (if (<= z 1.06e+191) t_1 (* z x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (z <= -1.15e+165) {
		tmp = z * x;
	} else if (z <= -2.85e-21) {
		tmp = t_1;
	} else if (z <= 3.8e-159) {
		tmp = fma(t, y, x);
	} else if (z <= 6e-13) {
		tmp = (t - x) * y;
	} else if (z <= 1.06e+191) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (z <= -1.15e+165)
		tmp = Float64(z * x);
	elseif (z <= -2.85e-21)
		tmp = t_1;
	elseif (z <= 3.8e-159)
		tmp = fma(t, y, x);
	elseif (z <= 6e-13)
		tmp = Float64(Float64(t - x) * y);
	elseif (z <= 1.06e+191)
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[z, -1.15e+165], N[(z * x), $MachinePrecision], If[LessEqual[z, -2.85e-21], t$95$1, If[LessEqual[z, 3.8e-159], N[(t * y + x), $MachinePrecision], If[LessEqual[z, 6e-13], N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 1.06e+191], t$95$1, N[(z * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.15000000000000008e165 or 1.06000000000000003e191 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 64.9%

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

   6. Taylor expanded in z around inf

      \[\leadsto z \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 61.6%

      \[\leadsto z \cdot x \]

   if -1.15000000000000008e165 < z < -2.8499999999999998e-21 or 5.99999999999999968e-13 < z < 1.06000000000000003e191

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 64.4%

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

   if -2.8499999999999998e-21 < z < 3.8000000000000001e-159

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 95.0%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(t, y, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 73.9%

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

   if 3.8000000000000001e-159 < z < 5.99999999999999968e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 71.7%

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

Alternative 3: 71.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+165}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-13}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+191}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= z -1.15e+165)
     (* z x)
     (if (<= z -1.35e-10)
       t_1
       (if (<= z 6.2e-13)
         (fma (- t x) y x)
         (if (<= z 1.06e+191) t_1 (* z x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (z <= -1.15e+165) {
		tmp = z * x;
	} else if (z <= -1.35e-10) {
		tmp = t_1;
	} else if (z <= 6.2e-13) {
		tmp = fma((t - x), y, x);
	} else if (z <= 1.06e+191) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (z <= -1.15e+165)
		tmp = Float64(z * x);
	elseif (z <= -1.35e-10)
		tmp = t_1;
	elseif (z <= 6.2e-13)
		tmp = fma(Float64(t - x), y, x);
	elseif (z <= 1.06e+191)
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[z, -1.15e+165], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.35e-10], t$95$1, If[LessEqual[z, 6.2e-13], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[z, 1.06e+191], t$95$1, N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15000000000000008e165 or 1.06000000000000003e191 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 64.9%

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

   6. Taylor expanded in z around inf

      \[\leadsto z \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 61.6%

      \[\leadsto z \cdot x \]

   if -1.15000000000000008e165 < z < -1.35e-10 or 6.1999999999999998e-13 < z < 1.06000000000000003e191

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 64.7%

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

   if -1.35e-10 < z < 6.1999999999999998e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 93.6%

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

Alternative 4: 57.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot y\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-258}:\\ \;\;\;\;\left(-z\right) \cdot t\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-296}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 150000000000:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t x) y)))
   (if (<= y -1.3e+14)
     t_1
     (if (<= y -7e-258)
       (* (- z) t)
       (if (<= y -1.75e-296)
         (* z x)
         (if (<= y 150000000000.0) (fma t y x) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t - x) * y;
	double tmp;
	if (y <= -1.3e+14) {
		tmp = t_1;
	} else if (y <= -7e-258) {
		tmp = -z * t;
	} else if (y <= -1.75e-296) {
		tmp = z * x;
	} else if (y <= 150000000000.0) {
		tmp = fma(t, y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t - x) * y)
	tmp = 0.0
	if (y <= -1.3e+14)
		tmp = t_1;
	elseif (y <= -7e-258)
		tmp = Float64(Float64(-z) * t);
	elseif (y <= -1.75e-296)
		tmp = Float64(z * x);
	elseif (y <= 150000000000.0)
		tmp = fma(t, y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.3e+14], t$95$1, If[LessEqual[y, -7e-258], N[((-z) * t), $MachinePrecision], If[LessEqual[y, -1.75e-296], N[(z * x), $MachinePrecision], If[LessEqual[y, 150000000000.0], N[(t * y + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.3e14 or 1.5e11 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 80.5%

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

   if -1.3e14 < y < -7.00000000000000003e-258

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. *-lft-identity N/A

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

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

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

      8. metadata-eval N/A

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

      9. distribute-rgt-out N/A

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

      10. associate-*r* N/A

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

      11. associate-+l+ N/A

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

      12. +-commutative N/A

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

      13. *-lft-identity N/A

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

      14. mul-1-neg N/A

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

      15. *-commutative N/A

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

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

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

      17. mul-1-neg N/A

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

      18. distribute-rgt-in N/A

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

   4. Applied rewrites 97.8%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 49.5%

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

   8. Taylor expanded in y around 0

      \[\leadsto \left(-1 \cdot z\right) \cdot t \]
   9. Step-by-step derivation

   10. Applied rewrites 43.0%

       \[\leadsto \left(-z\right) \cdot t \]

   if -7.00000000000000003e-258 < y < -1.7499999999999999e-296

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 85.0%

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

   6. Taylor expanded in z around inf

      \[\leadsto z \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 85.0%

      \[\leadsto z \cdot x \]

   if -1.7499999999999999e-296 < y < 1.5e11

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 50.2%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(t, y, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 50.3%

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

Alternative 5: 38.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+79}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-142}:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;z \leq -3.25 \cdot 10^{-243}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+54}:\\ \;\;\;\;t \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.15e+79)
   (* z x)
   (if (<= z -2.9e-142)
     (* t y)
     (if (<= z -3.25e-243) x (if (<= z 1.15e+54) (* t y) (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.15e+79) {
		tmp = z * x;
	} else if (z <= -2.9e-142) {
		tmp = t * y;
	} else if (z <= -3.25e-243) {
		tmp = x;
	} else if (z <= 1.15e+54) {
		tmp = t * y;
	} else {
		tmp = z * 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 (z <= (-2.15d+79)) then
        tmp = z * x
    else if (z <= (-2.9d-142)) then
        tmp = t * y
    else if (z <= (-3.25d-243)) then
        tmp = x
    else if (z <= 1.15d+54) then
        tmp = t * y
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.15e+79) {
		tmp = z * x;
	} else if (z <= -2.9e-142) {
		tmp = t * y;
	} else if (z <= -3.25e-243) {
		tmp = x;
	} else if (z <= 1.15e+54) {
		tmp = t * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.15e+79:
		tmp = z * x
	elif z <= -2.9e-142:
		tmp = t * y
	elif z <= -3.25e-243:
		tmp = x
	elif z <= 1.15e+54:
		tmp = t * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.15e+79)
		tmp = Float64(z * x);
	elseif (z <= -2.9e-142)
		tmp = Float64(t * y);
	elseif (z <= -3.25e-243)
		tmp = x;
	elseif (z <= 1.15e+54)
		tmp = Float64(t * y);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.15e+79)
		tmp = z * x;
	elseif (z <= -2.9e-142)
		tmp = t * y;
	elseif (z <= -3.25e-243)
		tmp = x;
	elseif (z <= 1.15e+54)
		tmp = t * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.15e+79], N[(z * x), $MachinePrecision], If[LessEqual[z, -2.9e-142], N[(t * y), $MachinePrecision], If[LessEqual[z, -3.25e-243], x, If[LessEqual[z, 1.15e+54], N[(t * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1500000000000002e79 or 1.14999999999999997e54 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 58.9%

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

   6. Taylor expanded in z around inf

      \[\leadsto z \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 49.5%

      \[\leadsto z \cdot x \]

   if -2.1500000000000002e79 < z < -2.8999999999999999e-142 or -3.25000000000000021e-243 < z < 1.14999999999999997e54

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 63.6%

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

   6. Taylor expanded in x around 0

      \[\leadsto t \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 40.1%

      \[\leadsto t \cdot y \]

   if -2.8999999999999999e-142 < z < -3.25000000000000021e-243

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 96.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 62.7%

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

Alternative 6: 83.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) \cdot \left(t - x\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-10}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- z) (- t x))))
   (if (<= z -2.1e+79)
     t_1
     (if (<= z -1.35e-10)
       (* (- y z) t)
       (if (<= z 1e+34) (fma (- t x) y x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -z * (t - x);
	double tmp;
	if (z <= -2.1e+79) {
		tmp = t_1;
	} else if (z <= -1.35e-10) {
		tmp = (y - z) * t;
	} else if (z <= 1e+34) {
		tmp = fma((t - x), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-z) * Float64(t - x))
	tmp = 0.0
	if (z <= -2.1e+79)
		tmp = t_1;
	elseif (z <= -1.35e-10)
		tmp = Float64(Float64(y - z) * t);
	elseif (z <= 1e+34)
		tmp = fma(Float64(t - x), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-z) * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+79], t$95$1, If[LessEqual[z, -1.35e-10], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 1e+34], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.10000000000000008e79 or 9.99999999999999946e33 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 84.2%

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

   if -2.10000000000000008e79 < z < -1.35e-10

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 81.8%

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

   if -1.35e-10 < z < 9.99999999999999946e33

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 92.5%

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

Alternative 7: 60.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+57}:\\ \;\;\;\;\mathsf{fma}\left(-x, y, x\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-80}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.1e+57)
   (fma (- x) y x)
   (if (<= x 2.5e-80) (* (- y z) t) (* (- t x) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.1e+57) {
		tmp = fma(-x, y, x);
	} else if (x <= 2.5e-80) {
		tmp = (y - z) * t;
	} else {
		tmp = (t - x) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.1e+57)
		tmp = fma(Float64(-x), y, x);
	elseif (x <= 2.5e-80)
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(Float64(t - x) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.1e+57], N[((-x) * y + x), $MachinePrecision], If[LessEqual[x, 2.5e-80], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1e57

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 65.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 64.1%

      \[\leadsto \mathsf{fma}\left(-x, y, x\right) \]

   if -1.1e57 < x < 2.5e-80

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 68.2%

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

   if 2.5e-80 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 60.3%

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

Alternative 8: 54.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+79} \lor \neg \left(z \leq 1.15 \cdot 10^{+54}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.15e+79) (not (<= z 1.15e+54))) (* z x) (fma t y x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.15e+79) || !(z <= 1.15e+54)) {
		tmp = z * x;
	} else {
		tmp = fma(t, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.15e+79) || !(z <= 1.15e+54))
		tmp = Float64(z * x);
	else
		tmp = fma(t, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.15e+79], N[Not[LessEqual[z, 1.15e+54]], $MachinePrecision]], N[(z * x), $MachinePrecision], N[(t * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1500000000000002e79 or 1.14999999999999997e54 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 58.9%

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

   6. Taylor expanded in z around inf

      \[\leadsto z \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 49.5%

      \[\leadsto z \cdot x \]

   if -2.1500000000000002e79 < z < 1.14999999999999997e54

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 86.1%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(t, y, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 63.8%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+79} \lor \neg \left(z \leq 1.15 \cdot 10^{+54}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+43} \lor \neg \left(z \leq 48000000000\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.1e+43) (not (<= z 48000000000.0))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.1e+43) || !(z <= 48000000000.0)) {
		tmp = z * x;
	} else {
		tmp = 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 ((z <= (-4.1d+43)) .or. (.not. (z <= 48000000000.0d0))) then
        tmp = z * x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.1e+43) || !(z <= 48000000000.0)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.1e+43) or not (z <= 48000000000.0):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.1e+43) || !(z <= 48000000000.0))
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.1e+43) || ~((z <= 48000000000.0)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.1e+43], N[Not[LessEqual[z, 48000000000.0]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.1e43 or 4.8e10 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 56.2%

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

   6. Taylor expanded in z around inf

      \[\leadsto z \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 44.9%

      \[\leadsto z \cdot x \]

   if -4.1e43 < z < 4.8e10

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 88.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 32.9%

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

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+43} \lor \neg \left(z \leq 48000000000\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 17.5% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in z around 0

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

5. Applied rewrites 61.5%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 19.1%

   \[\leadsto x \]
9. Add Preprocessing

Developer Target 1: 96.8% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

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 + ((t * (y - z)) + (-x * (y - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2025026 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (+ (* t (- y z)) (* (- x) (- y z)))))

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