Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 10.8s

Alternatives: 12

Speedup: 1.0×

• 35.1% 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

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

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((y - z) * (t - x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((y - z) * (t - x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 2: 49.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+132}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-204}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= y -3.5e+132)
     (* y t)
     (if (<= y -3.9e+49)
       (* y (- x))
       (if (<= y -5.5e-7)
         t_1
         (if (<= y 1.32e-204)
           (fma x z x)
           (if (<= y 2.1e-137)
             t_1
             (if (<= y 1.22e-23) (fma x z x) (* y t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -3.5e+132) {
		tmp = y * t;
	} else if (y <= -3.9e+49) {
		tmp = y * -x;
	} else if (y <= -5.5e-7) {
		tmp = t_1;
	} else if (y <= 1.32e-204) {
		tmp = fma(x, z, x);
	} else if (y <= 2.1e-137) {
		tmp = t_1;
	} else if (y <= 1.22e-23) {
		tmp = fma(x, z, x);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -3.5e+132)
		tmp = Float64(y * t);
	elseif (y <= -3.9e+49)
		tmp = Float64(y * Float64(-x));
	elseif (y <= -5.5e-7)
		tmp = t_1;
	elseif (y <= 1.32e-204)
		tmp = fma(x, z, x);
	elseif (y <= 2.1e-137)
		tmp = t_1;
	elseif (y <= 1.22e-23)
		tmp = fma(x, z, x);
	else
		tmp = Float64(y * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -3.5e+132], N[(y * t), $MachinePrecision], If[LessEqual[y, -3.9e+49], N[(y * (-x)), $MachinePrecision], If[LessEqual[y, -5.5e-7], t$95$1, If[LessEqual[y, 1.32e-204], N[(x * z + x), $MachinePrecision], If[LessEqual[y, 2.1e-137], t$95$1, If[LessEqual[y, 1.22e-23], N[(x * z + x), $MachinePrecision], N[(y * t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.5000000000000002e132 or 1.22000000000000007e-23 < y

   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

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 80.7

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

   5. Applied rewrites 80.7%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 43.3%

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

   if -3.5000000000000002e132 < y < -3.9000000000000001e49

   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. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. distribute-lft-in N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-neg.f64 99.0

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

   4. Applied rewrites 99.0%

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

   5. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. sub-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 72.1

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

   7. Applied rewrites 72.1%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 39.1%

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

   if -3.9000000000000001e49 < y < -5.5000000000000003e-7 or 1.32e-204 < y < 2.09999999999999992e-137

   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. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower--.f64 55.2

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

   5. Applied rewrites 55.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 33.7%

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

   if -5.5000000000000003e-7 < y < 1.32e-204 or 2.09999999999999992e-137 < y < 1.22000000000000007e-23

   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. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. distribute-lft-in N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-neg.f64 99.1

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

   4. Applied rewrites 99.1%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-in N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. lower--.f64 91.4

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

   7. Applied rewrites 91.4%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 59.4%

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

real(8) function code(x, y, z, t)
    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 2024223 
(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))))