Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 2.7s

Alternatives: 13

Speedup: 1.2×

• 34.6% 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. 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. lower-fma.f64 N/A

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

   7. lift--.f64 N/A

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

   8. lift--.f64 100.0

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

4. Applied rewrites 100.0%

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

Alternative 2: 36.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y - z \leq -4 \cdot 10^{+164}:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;y - z \leq -2 \cdot 10^{+34}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y - z \leq 5 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;y - z \leq 4 \cdot 10^{+101}:\\ \;\;\;\;t \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (- y z) -4e+164)
   (* t y)
   (if (<= (- y z) -2e+34)
     (* z x)
     (if (<= (- y z) 5e-40) x (if (<= (- y z) 4e+101) (* t y) (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y - z) <= -4e+164) {
		tmp = t * y;
	} else if ((y - z) <= -2e+34) {
		tmp = z * x;
	} else if ((y - z) <= 5e-40) {
		tmp = x;
	} else if ((y - z) <= 4e+101) {
		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 ((y - z) <= (-4d+164)) then
        tmp = t * y
    else if ((y - z) <= (-2d+34)) then
        tmp = z * x
    else if ((y - z) <= 5d-40) then
        tmp = x
    else if ((y - z) <= 4d+101) 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 ((y - z) <= -4e+164) {
		tmp = t * y;
	} else if ((y - z) <= -2e+34) {
		tmp = z * x;
	} else if ((y - z) <= 5e-40) {
		tmp = x;
	} else if ((y - z) <= 4e+101) {
		tmp = t * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y - z) <= -4e+164:
		tmp = t * y
	elif (y - z) <= -2e+34:
		tmp = z * x
	elif (y - z) <= 5e-40:
		tmp = x
	elif (y - z) <= 4e+101:
		tmp = t * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(y - z) <= -4e+164)
		tmp = Float64(t * y);
	elseif (Float64(y - z) <= -2e+34)
		tmp = Float64(z * x);
	elseif (Float64(y - z) <= 5e-40)
		tmp = x;
	elseif (Float64(y - z) <= 4e+101)
		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 ((y - z) <= -4e+164)
		tmp = t * y;
	elseif ((y - z) <= -2e+34)
		tmp = z * x;
	elseif ((y - z) <= 5e-40)
		tmp = x;
	elseif ((y - z) <= 4e+101)
		tmp = t * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(y - z), $MachinePrecision], -4e+164], N[(t * y), $MachinePrecision], If[LessEqual[N[(y - z), $MachinePrecision], -2e+34], N[(z * x), $MachinePrecision], If[LessEqual[N[(y - z), $MachinePrecision], 5e-40], x, If[LessEqual[N[(y - z), $MachinePrecision], 4e+101], N[(t * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 y z) < -4e164 or 4.99999999999999965e-40 < (-.f64 y z) < 3.9999999999999999e101

   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. lift--.f64 50.4

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

   5. Applied rewrites 50.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 27.9%

      \[\leadsto t \cdot y \]

   if -4e164 < (-.f64 y z) < -1.99999999999999989e34 or 3.9999999999999999e101 < (-.f64 y z)

   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. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lift--.f64 52.8

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

   5. Applied rewrites 52.8%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 28.8

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

   8. Applied rewrites 28.8%

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

   9. Taylor expanded in z around inf

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

       1. *-commutative N/A

          \[\leadsto z \cdot x \]

       2. lower-*.f64 28.7

          \[\leadsto z \cdot x \]

   11. Applied rewrites 28.7%

       \[\leadsto z \cdot x \]

   if -1.99999999999999989e34 < (-.f64 y z) < 4.99999999999999965e-40

   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. lift--.f64 78.2

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

   5. Applied rewrites 78.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 59.1%

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

Alternative 3: 69.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+105}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -0.0132:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+119}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= z -3.3e+146)
     t_1
     (if (<= z -5.5e+105)
       (* z x)
       (if (<= z -0.0132)
         t_1
         (if (<= z 1.32e+119) (fma (- t x) y x) (* z x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (z <= -3.3e+146) {
		tmp = t_1;
	} else if (z <= -5.5e+105) {
		tmp = z * x;
	} else if (z <= -0.0132) {
		tmp = t_1;
	} else if (z <= 1.32e+119) {
		tmp = fma((t - x), y, x);
	} 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 <= -3.3e+146)
		tmp = t_1;
	elseif (z <= -5.5e+105)
		tmp = Float64(z * x);
	elseif (z <= -0.0132)
		tmp = t_1;
	elseif (z <= 1.32e+119)
		tmp = fma(Float64(t - x), y, x);
	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, -3.3e+146], t$95$1, If[LessEqual[z, -5.5e+105], N[(z * x), $MachinePrecision], If[LessEqual[z, -0.0132], t$95$1, If[LessEqual[z, 1.32e+119], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.30000000000000016e146 or -5.49999999999999979e105 < z < -0.0132

   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. lift--.f64 53.8

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

   5. Applied rewrites 53.8%

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

   if -3.30000000000000016e146 < z < -5.49999999999999979e105 or 1.32e119 < z

   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. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lift--.f64 85.8

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

   5. Applied rewrites 85.8%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 46.0

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

   8. Applied rewrites 46.0%

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

   9. Taylor expanded in z around inf

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

       1. *-commutative N/A

          \[\leadsto z \cdot x \]

       2. lower-*.f64 46.0

          \[\leadsto z \cdot x \]

   11. Applied rewrites 46.0%

       \[\leadsto z \cdot x \]

   if -0.0132 < z < 1.32e119

   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. lift--.f64 83.0

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

   5. Applied rewrites 83.0%

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

Alternative 4: 67.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot y\\ t_2 := \left(y - z\right) \cdot t\\ \mathbf{if}\;y \leq -3 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-89}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;y \leq 0.000116:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t x) y)) (t_2 (* (- y z) t)))
   (if (<= y -3e+88)
     t_1
     (if (<= y -5.2e-15)
       t_2
       (if (<= y 1.08e-89) (fma x z x) (if (<= y 0.000116) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t - x) * y;
	double t_2 = (y - z) * t;
	double tmp;
	if (y <= -3e+88) {
		tmp = t_1;
	} else if (y <= -5.2e-15) {
		tmp = t_2;
	} else if (y <= 1.08e-89) {
		tmp = fma(x, z, x);
	} else if (y <= 0.000116) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t - x) * y)
	t_2 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (y <= -3e+88)
		tmp = t_1;
	elseif (y <= -5.2e-15)
		tmp = t_2;
	elseif (y <= 1.08e-89)
		tmp = fma(x, z, x);
	elseif (y <= 0.000116)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -3e+88], t$95$1, If[LessEqual[y, -5.2e-15], t$95$2, If[LessEqual[y, 1.08e-89], N[(x * z + x), $MachinePrecision], If[LessEqual[y, 0.000116], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.00000000000000005e88 or 1.16e-4 < 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. lift--.f64 80.9

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

   5. Applied rewrites 80.9%

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

   if -3.00000000000000005e88 < y < -5.20000000000000009e-15 or 1.07999999999999999e-89 < y < 1.16e-4

   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. lift--.f64 51.0

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

   5. Applied rewrites 51.0%

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

   if -5.20000000000000009e-15 < y < 1.07999999999999999e-89

   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. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lift--.f64 93.1

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

   5. Applied rewrites 93.1%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 59.7

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

   8. Applied rewrites 59.7%

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

Alternative 5: 53.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+147}:\\ \;\;\;\;\left(-t\right) \cdot z\\ \mathbf{elif}\;z \leq -0.058:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+60}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2e+147)
   (* (- t) z)
   (if (<= z -0.058) (fma x z x) (if (<= z 5e+60) (fma t y x) (* z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2e+147) {
		tmp = -t * z;
	} else if (z <= -0.058) {
		tmp = fma(x, z, x);
	} else if (z <= 5e+60) {
		tmp = fma(t, y, x);
	} else {
		tmp = z * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2e+147)
		tmp = Float64(Float64(-t) * z);
	elseif (z <= -0.058)
		tmp = fma(x, z, x);
	elseif (z <= 5e+60)
		tmp = fma(t, y, x);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2e+147], N[((-t) * z), $MachinePrecision], If[LessEqual[z, -0.058], N[(x * z + x), $MachinePrecision], If[LessEqual[z, 5e+60], N[(t * y + x), $MachinePrecision], N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2e147

   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. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lift--.f64 90.0

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

   5. Applied rewrites 90.0%

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

   6. Taylor expanded in x around 0

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 49.3

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

   8. Applied rewrites 49.3%

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

   if -2e147 < z < -0.0580000000000000029

   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. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lift--.f64 67.4

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

   5. Applied rewrites 67.4%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 33.0

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

   8. Applied rewrites 33.0%

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

   if -0.0580000000000000029 < z < 4.99999999999999975e60

   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. lift--.f64 86.9

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

   5. Applied rewrites 86.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 62.6%

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

   if 4.99999999999999975e60 < z

   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. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lift--.f64 82.0

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

   5. Applied rewrites 82.0%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 44.6

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

   8. Applied rewrites 44.6%

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

   9. Taylor expanded in z around inf

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

       1. *-commutative N/A

          \[\leadsto z \cdot x \]

       2. lower-*.f64 44.6

          \[\leadsto z \cdot x \]

   11. Applied rewrites 44.6%

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

Alternative 6: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-z, t - x, x\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+51}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (- z) (- t x) x)))
   (if (<= z -2e-7) t_1 (if (<= z 4.2e+51) (fma (- t x) y x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(-z, (t - x), x);
	double tmp;
	if (z <= -2e-7) {
		tmp = t_1;
	} else if (z <= 4.2e+51) {
		tmp = fma((t - x), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(-z), Float64(t - x), x)
	tmp = 0.0
	if (z <= -2e-7)
		tmp = t_1;
	elseif (z <= 4.2e+51)
		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] + x), $MachinePrecision]}, If[LessEqual[z, -2e-7], t$95$1, If[LessEqual[z, 4.2e+51], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9999999999999999e-7 or 4.2000000000000002e51 < z

   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. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lift--.f64 79.8

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

   5. Applied rewrites 79.8%

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

   if -1.9999999999999999e-7 < z < 4.2000000000000002e51

   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. lift--.f64 87.6

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

   5. Applied rewrites 87.6%

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

Alternative 7: 83.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) \cdot \left(t - x\right)\\ \mathbf{if}\;z \leq -3200000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+51}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- z) (- t x))))
   (if (<= z -3200000000000.0) t_1 (if (<= z 4.2e+51) (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 <= -3200000000000.0) {
		tmp = t_1;
	} else if (z <= 4.2e+51) {
		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 <= -3200000000000.0)
		tmp = t_1;
	elseif (z <= 4.2e+51)
		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, -3200000000000.0], t$95$1, If[LessEqual[z, 4.2e+51], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2e12 or 4.2000000000000002e51 < 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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 80.7

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

   5. Applied rewrites 80.7%

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

   if -3.2e12 < z < 4.2000000000000002e51

   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. lift--.f64 86.4

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

   5. Applied rewrites 86.4%

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

Alternative 8: 70.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot y\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(-z, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t x) y)))
   (if (<= y -2.8e+66) t_1 (if (<= y 3.9e-28) (fma (- z) t x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t - x) * y;
	double tmp;
	if (y <= -2.8e+66) {
		tmp = t_1;
	} else if (y <= 3.9e-28) {
		tmp = fma(-z, t, 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 <= -2.8e+66)
		tmp = t_1;
	elseif (y <= 3.9e-28)
		tmp = fma(Float64(-z), t, 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, -2.8e+66], t$95$1, If[LessEqual[y, 3.9e-28], N[((-z) * t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8000000000000001e66 or 3.89999999999999999e-28 < 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. lift--.f64 78.3

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

   5. Applied rewrites 78.3%

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

   if -2.8000000000000001e66 < y < 3.89999999999999999e-28

   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. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lift--.f64 87.2

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

   5. Applied rewrites 87.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 64.1%

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

Alternative 9: 68.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot y\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.4:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t x) y)))
   (if (<= y -4.5e-13) t_1 (if (<= y 5.4) (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 <= -4.5e-13) {
		tmp = t_1;
	} else if (y <= 5.4) {
		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 <= -4.5e-13)
		tmp = t_1;
	elseif (y <= 5.4)
		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, -4.5e-13], t$95$1, If[LessEqual[y, 5.4], N[(x * z + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5e-13 or 5.4000000000000004 < 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. lift--.f64 77.7

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

   5. Applied rewrites 77.7%

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

   if -4.5e-13 < y < 5.4000000000000004

   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. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lift--.f64 91.2

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

   5. Applied rewrites 91.2%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 58.5

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

   8. Applied rewrites 58.5%

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

Alternative 10: 53.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.058:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+60}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.058) (fma x z x) (if (<= z 5e+60) (fma t y x) (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.058) {
		tmp = fma(x, z, x);
	} else if (z <= 5e+60) {
		tmp = fma(t, y, x);
	} else {
		tmp = z * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.058)
		tmp = fma(x, z, x);
	elseif (z <= 5e+60)
		tmp = fma(t, y, x);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.058], N[(x * z + x), $MachinePrecision], If[LessEqual[z, 5e+60], N[(t * y + x), $MachinePrecision], N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0580000000000000029

   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. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lift--.f64 79.4

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

   5. Applied rewrites 79.4%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 41.4

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

   8. Applied rewrites 41.4%

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

   if -0.0580000000000000029 < z < 4.99999999999999975e60

   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. lift--.f64 86.9

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

   5. Applied rewrites 86.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 62.6%

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

   if 4.99999999999999975e60 < z

   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. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lift--.f64 82.0

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

   5. Applied rewrites 82.0%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 44.6

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

   8. Applied rewrites 44.6%

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

   9. Taylor expanded in z around inf

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

       1. *-commutative N/A

          \[\leadsto z \cdot x \]

       2. lower-*.f64 44.6

          \[\leadsto z \cdot x \]

   11. Applied rewrites 44.6%

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

Alternative 11: 45.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+80}:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;t \leq 7.9 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.5e+80) (* t y) (if (<= t 7.9e+80) (fma x z x) (* t y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.5e+80) {
		tmp = t * y;
	} else if (t <= 7.9e+80) {
		tmp = fma(x, z, x);
	} else {
		tmp = t * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.5e+80)
		tmp = Float64(t * y);
	elseif (t <= 7.9e+80)
		tmp = fma(x, z, x);
	else
		tmp = Float64(t * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.5e+80], N[(t * y), $MachinePrecision], If[LessEqual[t, 7.9e+80], N[(x * z + x), $MachinePrecision], N[(t * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.49999999999999994e80 or 7.89999999999999999e80 < t

   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. lift--.f64 48.9

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

   5. Applied rewrites 48.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 43.3%

      \[\leadsto t \cdot y \]

   if -3.49999999999999994e80 < t < 7.89999999999999999e80

   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. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lift--.f64 61.1

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

   5. Applied rewrites 61.1%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 47.3

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

   8. Applied rewrites 47.3%

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

Alternative 12: 37.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.0) (* z x) (if (<= z 1.15e+17) x (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.0) {
		tmp = z * x;
	} else if (z <= 1.15e+17) {
		tmp = x;
	} 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 <= (-1.0d0)) then
        tmp = z * x
    else if (z <= 1.15d+17) then
        tmp = x
    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 <= -1.0) {
		tmp = z * x;
	} else if (z <= 1.15e+17) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.0:
		tmp = z * x
	elif z <= 1.15e+17:
		tmp = x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(z * x);
	elseif (z <= 1.15e+17)
		tmp = x;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = z * x;
	elseif (z <= 1.15e+17)
		tmp = x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.0], N[(z * x), $MachinePrecision], If[LessEqual[z, 1.15e+17], x, N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1.15e17 < z

   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. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lift--.f64 78.7

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

   5. Applied rewrites 78.7%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 41.8

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

   8. Applied rewrites 41.8%

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

   9. Taylor expanded in z around inf

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

       1. *-commutative N/A

          \[\leadsto z \cdot x \]

       2. lower-*.f64 41.5

          \[\leadsto z \cdot x \]

   11. Applied rewrites 41.5%

       \[\leadsto z \cdot x \]

   if -1 < z < 1.15e17

   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. lift--.f64 89.2

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

   5. Applied rewrites 89.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 32.7%

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

Alternative 13: 18.2% 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

   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. lift--.f64 60.7

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

5. Applied rewrites 60.7%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 18.2%

   \[\leadsto x \]
9. Add Preprocessing

Developer Target 1: 96.3% 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 2025091 
(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))))