Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23

Percentage Accurate: 99.9% → 99.9%

Time: 2.4s

Alternatives: 4

Speedup: 1.1×

• 70.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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) * y) + t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	(((x * y) + z) * y) + t
END code

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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) * y) + t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	(((x * y) + z) * y) + t
END code

Alternative 1: 99.9% accurate, 1.1× speedup

Math

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

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (fma y (fma y x z) t))

C

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

Julia

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

Wolfram

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

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	(y * ((y * x) + z)) + t
END code

Derivation

1. Initial program 99.9%

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

3. Applied rewrites 99.9%

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

Alternative 2: 89.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y, x, z\right) \cdot y\\ \mathbf{if}\;y \leq -362737.36445094895:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 27842210377009184:\\ \;\;\;\;\mathsf{fma}\left(y, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* (fma y x z) y)))
  (if (<= y -362737.36445094895)
    t_1
    (if (<= y 27842210377009184.0) (fma y z t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(y, x, z) * y;
	double tmp;
	if (y <= -362737.36445094895) {
		tmp = t_1;
	} else if (y <= 27842210377009184.0) {
		tmp = fma(y, z, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(y, x, z) * y)
	tmp = 0.0
	if (y <= -362737.36445094895)
		tmp = t_1;
	elseif (y <= 27842210377009184.0)
		tmp = fma(y, z, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * x + z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -362737.36445094895], t$95$1, If[LessEqual[y, 27842210377009184.0], N[(y * z + t), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = (((y * x) + z) * y) IN
		LET tmp_1 = IF (y <= (27842210377009184)) THEN ((y * z) + t) ELSE t_1 ENDIF IN
		LET tmp = IF (y <= (-3627373644509489531628787517547607421875e-34)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -362737.36445094895 or 27842210377009184 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 92.3%

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

   6. Applied rewrites 92.2%

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

   7. Taylor expanded in t around 0

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

   9. Applied rewrites 55.4%

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

   11. Applied rewrites 63.2%

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

   if -362737.36445094895 < y < 27842210377009184

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto z \cdot y + t \]
   3. Step-by-step derivation

   4. Applied rewrites 65.7%

      \[\leadsto z \cdot y + t \]
   5. Step-by-step derivation

   6. Applied rewrites 65.7%

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

Alternative 3: 65.7% accurate, 2.0× speedup

Math

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

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (fma y z t))

C

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

Julia

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

Wolfram

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

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	(y * z) + t
END code

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0

   \[\leadsto z \cdot y + t \]
3. Step-by-step derivation

4. Applied rewrites 65.7%

   \[\leadsto z \cdot y + t \]
5. Step-by-step derivation

6. Applied rewrites 65.7%

   \[\leadsto \mathsf{fma}\left(y, z, t\right) \]
7. Add Preprocessing

Alternative 4: 38.6% accurate, 12.2× speedup

Math

\[t \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	t
END code

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0

   \[\leadsto t \]
3. Step-by-step derivation

4. Applied rewrites 38.6%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))