Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 5.2s

Alternatives: 11

Speedup: 1.2×

• 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, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 100.0

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

4. Applied rewrites 100.0%

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

Alternative 2: 71.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - t\right) \cdot z\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-20}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-154}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \mathbf{elif}\;z \leq 10^{+34}:\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x t) z)))
   (if (<= z -2.1e+79)
     t_1
     (if (<= z -2.4e-20)
       (* (- y z) t)
       (if (<= z 6e-154) (fma t y x) (if (<= z 1e+34) (* (- t x) y) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - t) * z;
	double tmp;
	if (z <= -2.1e+79) {
		tmp = t_1;
	} else if (z <= -2.4e-20) {
		tmp = (y - z) * t;
	} else if (z <= 6e-154) {
		tmp = fma(t, y, x);
	} else if (z <= 1e+34) {
		tmp = (t - x) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - t) * z)
	tmp = 0.0
	if (z <= -2.1e+79)
		tmp = t_1;
	elseif (z <= -2.4e-20)
		tmp = Float64(Float64(y - z) * t);
	elseif (z <= 6e-154)
		tmp = fma(t, y, x);
	elseif (z <= 1e+34)
		tmp = Float64(Float64(t - x) * y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -2.1e+79], t$95$1, If[LessEqual[z, -2.4e-20], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 6e-154], N[(t * y + x), $MachinePrecision], If[LessEqual[z, 1e+34], N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

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

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \left(\mathsf{neg}\left(t\right)\right)\right) \cdot z \]

      11. remove-double-neg N/A

          \[\leadsto \left(x + \left(\mathsf{neg}\left(t\right)\right)\right) \cdot z \]

      12. mul-1-neg N/A

          \[\leadsto \left(x + -1 \cdot t\right) \cdot z \]

      13. metadata-eval N/A

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

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

          \[\leadsto \left(x - 1 \cdot t\right) \cdot z \]

      15. *-lft-identity N/A

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

      16. lower--.f64 84.2

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

   7. Applied rewrites 84.2%

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

   if -2.10000000000000008e79 < z < -2.39999999999999993e-20

   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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 78.6

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

   5. Applied rewrites 78.6%

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

   if -2.39999999999999993e-20 < z < 6.0000000000000005e-154

   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

      1. +-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(t - x\right) \cdot y + x \]

      3. lower-fma.f64 N/A

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

      4. lower--.f64 95.0

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

   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 6.0000000000000005e-154 < 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 y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.8

         \[\leadsto \left(t - x\right) \cdot y \]

   5. Applied rewrites 71.8%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+79}:\\ \;\;\;\;\left(x - t\right) \cdot z\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-20}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-154}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \mathbf{elif}\;z \leq 10^{+34}:\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(x - t\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 38.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+79}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-141}:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;z \leq -4.55 \cdot 10^{-243}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+54}:\\ \;\;\;\;t \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.15e+79)
   (* x z)
   (if (<= z -3.8e-141)
     (* t y)
     (if (<= z -4.55e-243) x (if (<= z 1.9e+54) (* t y) (* x z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.15e+79) {
		tmp = x * z;
	} else if (z <= -3.8e-141) {
		tmp = t * y;
	} else if (z <= -4.55e-243) {
		tmp = x;
	} else if (z <= 1.9e+54) {
		tmp = t * y;
	} else {
		tmp = x * z;
	}
	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 = x * z
    else if (z <= (-3.8d-141)) then
        tmp = t * y
    else if (z <= (-4.55d-243)) then
        tmp = x
    else if (z <= 1.9d+54) then
        tmp = t * y
    else
        tmp = x * z
    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 = x * z;
	} else if (z <= -3.8e-141) {
		tmp = t * y;
	} else if (z <= -4.55e-243) {
		tmp = x;
	} else if (z <= 1.9e+54) {
		tmp = t * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.15e+79:
		tmp = x * z
	elif z <= -3.8e-141:
		tmp = t * y
	elif z <= -4.55e-243:
		tmp = x
	elif z <= 1.9e+54:
		tmp = t * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.15e+79)
		tmp = Float64(x * z);
	elseif (z <= -3.8e-141)
		tmp = Float64(t * y);
	elseif (z <= -4.55e-243)
		tmp = x;
	elseif (z <= 1.9e+54)
		tmp = Float64(t * y);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.15e+79)
		tmp = x * z;
	elseif (z <= -3.8e-141)
		tmp = t * y;
	elseif (z <= -4.55e-243)
		tmp = x;
	elseif (z <= 1.9e+54)
		tmp = t * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.15e+79], N[(x * z), $MachinePrecision], If[LessEqual[z, -3.8e-141], N[(t * y), $MachinePrecision], If[LessEqual[z, -4.55e-243], x, If[LessEqual[z, 1.9e+54], N[(t * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1500000000000002e79 or 1.9000000000000001e54 < z

   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. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

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

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \left(\mathsf{neg}\left(t\right)\right)\right) \cdot z \]

      11. remove-double-neg N/A

          \[\leadsto \left(x + \left(\mathsf{neg}\left(t\right)\right)\right) \cdot z \]

      12. mul-1-neg N/A

          \[\leadsto \left(x + -1 \cdot t\right) \cdot z \]

      13. metadata-eval N/A

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

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

          \[\leadsto \left(x - 1 \cdot t\right) \cdot z \]

      15. *-lft-identity N/A

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

      16. lower--.f64 85.0

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

   7. Applied rewrites 85.0%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 49.5%

       \[\leadsto x \cdot z \]

   if -2.1500000000000002e79 < z < -3.79999999999999987e-141 or -4.55000000000000009e-243 < z < 1.9000000000000001e54

   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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 63.6

         \[\leadsto \left(t - x\right) \cdot y \]

   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 -3.79999999999999987e-141 < z < -4.55000000000000009e-243

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. fp-cancel-sub-sign N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 66.8

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

   5. Applied rewrites 66.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 62.7%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+79}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-141}:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;z \leq -4.55 \cdot 10^{-243}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+54}:\\ \;\;\;\;t \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.4% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x t) z)))
   (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 = (x - t) * z;
	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(x - t) * z)
	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[(N[(x - t), $MachinePrecision] * z), $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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

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

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \left(\mathsf{neg}\left(t\right)\right)\right) \cdot z \]

      11. remove-double-neg N/A

          \[\leadsto \left(x + \left(\mathsf{neg}\left(t\right)\right)\right) \cdot z \]

      12. mul-1-neg N/A

          \[\leadsto \left(x + -1 \cdot t\right) \cdot z \]

      13. metadata-eval N/A

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

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

          \[\leadsto \left(x - 1 \cdot t\right) \cdot z \]

      15. *-lft-identity N/A

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

      16. lower--.f64 84.2

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

   7. Applied rewrites 84.2%

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

   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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 81.8

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

   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

      1. +-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(t - x\right) \cdot y + x \]

      3. lower-fma.f64 N/A

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

      4. lower--.f64 92.5

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

   5. Applied rewrites 92.5%

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

4. Final simplification 88.2%

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

Alternative 5: 67.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot y\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-19}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t x) y)))
   (if (<= y -1.2e+40)
     t_1
     (if (<= y -1.05e-19) (* (- y z) t) (if (<= y 6.5e+32) (fma x z x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t - x) * y;
	double tmp;
	if (y <= -1.2e+40) {
		tmp = t_1;
	} else if (y <= -1.05e-19) {
		tmp = (y - z) * t;
	} else if (y <= 6.5e+32) {
		tmp = fma(x, z, 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 <= -1.2e+40)
		tmp = t_1;
	elseif (y <= -1.05e-19)
		tmp = Float64(Float64(y - z) * t);
	elseif (y <= 6.5e+32)
		tmp = fma(x, z, 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, -1.2e+40], t$95$1, If[LessEqual[y, -1.05e-19], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 6.5e+32], N[(x * z + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2e40 or 6.4999999999999994e32 < 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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 82.7

         \[\leadsto \left(t - x\right) \cdot y \]

   5. Applied rewrites 82.7%

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

   if -1.2e40 < y < -1.0499999999999999e-19

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 82.4

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

   5. Applied rewrites 82.4%

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

   if -1.0499999999999999e-19 < y < 6.4999999999999994e32

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. fp-cancel-sub-sign N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 90.7

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

   5. Applied rewrites 90.7%

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

   6. Taylor expanded in x around inf

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

      1. distribute-rgt-out-- N/A

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

      2. *-lft-identity N/A

         \[\leadsto x - \left(-1 \cdot z\right) \cdot x \]

      3. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(z\right)\right) \cdot x \]

      4. fp-cancel-sign-sub N/A

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

      5. *-commutative N/A

         \[\leadsto x + x \cdot z \]

      6. +-commutative N/A

         \[\leadsto x \cdot z + x \]

      7. lower-fma.f64 61.5

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

   8. Applied rewrites 61.5%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-19}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+38} \lor \neg \left(y \leq 1.85 \cdot 10^{-16}\right):\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.9e+38) (not (<= y 1.85e-16))) (* (- t x) y) (- x (* t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.9e+38) || !(y <= 1.85e-16)) {
		tmp = (t - x) * y;
	} else {
		tmp = x - (t * z);
	}
	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 ((y <= (-2.9d+38)) .or. (.not. (y <= 1.85d-16))) then
        tmp = (t - x) * y
    else
        tmp = x - (t * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.9e+38) || !(y <= 1.85e-16)) {
		tmp = (t - x) * y;
	} else {
		tmp = x - (t * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.9e+38) or not (y <= 1.85e-16):
		tmp = (t - x) * y
	else:
		tmp = x - (t * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.9e+38) || !(y <= 1.85e-16))
		tmp = Float64(Float64(t - x) * y);
	else
		tmp = Float64(x - Float64(t * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.9e+38) || ~((y <= 1.85e-16)))
		tmp = (t - x) * y;
	else
		tmp = x - (t * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.9e+38], N[Not[LessEqual[y, 1.85e-16]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision], N[(x - N[(t * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.90000000000000007e38 or 1.85e-16 < 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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.4

         \[\leadsto \left(t - x\right) \cdot y \]

   5. Applied rewrites 79.4%

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

   if -2.90000000000000007e38 < y < 1.85e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. fp-cancel-sub-sign N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 91.3

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

   5. Applied rewrites 91.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 68.1%

      \[\leadsto x - t \cdot z \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+38} \lor \neg \left(y \leq 1.85 \cdot 10^{-16}\right):\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{-18} \lor \neg \left(y \leq 6.5 \cdot 10^{+32}\right):\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.32e-18) (not (<= y 6.5e+32))) (* (- t x) y) (fma x z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.32e-18) || !(y <= 6.5e+32)) {
		tmp = (t - x) * y;
	} else {
		tmp = fma(x, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.32e-18) || !(y <= 6.5e+32))
		tmp = Float64(Float64(t - x) * y);
	else
		tmp = fma(x, z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.32e-18], N[Not[LessEqual[y, 6.5e+32]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision], N[(x * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3199999999999999e-18 or 6.4999999999999994e32 < 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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 78.4

         \[\leadsto \left(t - x\right) \cdot y \]

   5. Applied rewrites 78.4%

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

   if -1.3199999999999999e-18 < y < 6.4999999999999994e32

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. fp-cancel-sub-sign N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 90.7

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

   5. Applied rewrites 90.7%

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

   6. Taylor expanded in x around inf

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

      1. distribute-rgt-out-- N/A

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

      2. *-lft-identity N/A

         \[\leadsto x - \left(-1 \cdot z\right) \cdot x \]

      3. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(z\right)\right) \cdot x \]

      4. fp-cancel-sign-sub N/A

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

      5. *-commutative N/A

         \[\leadsto x + x \cdot z \]

      6. +-commutative N/A

         \[\leadsto x \cdot z + x \]

      7. lower-fma.f64 61.5

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

   8. Applied rewrites 61.5%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{-18} \lor \neg \left(y \leq 6.5 \cdot 10^{+32}\right):\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+79} \lor \neg \left(z \leq 3 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.15e+79) (not (<= z 3e+54))) (* x z) (fma t y x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.15e+79) || !(z <= 3e+54)) {
		tmp = x * z;
	} else {
		tmp = fma(t, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.15e+79) || !(z <= 3e+54))
		tmp = Float64(x * z);
	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, 3e+54]], $MachinePrecision]], N[(x * z), $MachinePrecision], N[(t * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1500000000000002e79 or 2.9999999999999999e54 < z

   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. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

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

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \left(\mathsf{neg}\left(t\right)\right)\right) \cdot z \]

      11. remove-double-neg N/A

          \[\leadsto \left(x + \left(\mathsf{neg}\left(t\right)\right)\right) \cdot z \]

      12. mul-1-neg N/A

          \[\leadsto \left(x + -1 \cdot t\right) \cdot z \]

      13. metadata-eval N/A

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

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

          \[\leadsto \left(x - 1 \cdot t\right) \cdot z \]

      15. *-lft-identity N/A

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

      16. lower--.f64 85.0

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

   7. Applied rewrites 85.0%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 49.5%

       \[\leadsto x \cdot z \]

   if -2.1500000000000002e79 < z < 2.9999999999999999e54

   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

      1. +-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(t - x\right) \cdot y + x \]

      3. lower-fma.f64 N/A

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

      4. lower--.f64 86.1

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

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+79} \lor \neg \left(z \leq 3 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+56} \lor \neg \left(y \leq 7.5 \cdot 10^{+35}\right):\\ \;\;\;\;t \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.5e+56) (not (<= y 7.5e+35))) (* t y) (fma x z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.5e+56) || !(y <= 7.5e+35)) {
		tmp = t * y;
	} else {
		tmp = fma(x, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.5e+56) || !(y <= 7.5e+35))
		tmp = Float64(t * y);
	else
		tmp = fma(x, z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.5e+56], N[Not[LessEqual[y, 7.5e+35]], $MachinePrecision]], N[(t * y), $MachinePrecision], N[(x * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5000000000000002e56 or 7.4999999999999999e35 < 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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 82.3

         \[\leadsto \left(t - x\right) \cdot y \]

   5. Applied rewrites 82.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 48.0%

      \[\leadsto t \cdot y \]

   if -5.5000000000000002e56 < y < 7.4999999999999999e35

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. fp-cancel-sub-sign N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 87.3

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

   5. Applied rewrites 87.3%

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

   6. Taylor expanded in x around inf

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

      1. distribute-rgt-out-- N/A

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

      2. *-lft-identity N/A

         \[\leadsto x - \left(-1 \cdot z\right) \cdot x \]

      3. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(z\right)\right) \cdot x \]

      4. fp-cancel-sign-sub N/A

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

      5. *-commutative N/A

         \[\leadsto x + x \cdot z \]

      6. +-commutative N/A

         \[\leadsto x \cdot z + x \]

      7. lower-fma.f64 57.6

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

   8. Applied rewrites 57.6%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+56} \lor \neg \left(y \leq 7.5 \cdot 10^{+35}\right):\\ \;\;\;\;t \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-37} \lor \neg \left(y \leq 5 \cdot 10^{-31}\right):\\ \;\;\;\;t \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.35e-37) (not (<= y 5e-31))) (* t y) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.35e-37) || !(y <= 5e-31)) {
		tmp = t * y;
	} 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 ((y <= (-1.35d-37)) .or. (.not. (y <= 5d-31))) then
        tmp = t * y
    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 ((y <= -1.35e-37) || !(y <= 5e-31)) {
		tmp = t * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.35e-37) or not (y <= 5e-31):
		tmp = t * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.35e-37) || !(y <= 5e-31))
		tmp = Float64(t * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.35e-37) || ~((y <= 5e-31)))
		tmp = t * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.35e-37], N[Not[LessEqual[y, 5e-31]], $MachinePrecision]], N[(t * y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.35000000000000008e-37 or 5e-31 < 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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 74.5

         \[\leadsto \left(t - x\right) \cdot y \]

   5. Applied rewrites 74.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 43.5%

      \[\leadsto t \cdot y \]

   if -1.35000000000000008e-37 < y < 5e-31

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. fp-cancel-sub-sign N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 94.8

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

   5. Applied rewrites 94.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 38.8%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-37} \lor \neg \left(y \leq 5 \cdot 10^{-31}\right):\\ \;\;\;\;t \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 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 y around 0

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

   1. associate-*r* N/A

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

   2. mul-1-neg N/A

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

   3. fp-cancel-sub-sign N/A

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

   4. lower--.f64 N/A

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

   5. *-commutative N/A

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

   6. lower-*.f64 N/A

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

   7. lower--.f64 59.9

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

5. Applied rewrites 59.9%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 19.1%

   \[\leadsto x \]

9. Final simplification 19.1%

   \[\leadsto x \]
10. 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))))