Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2

Percentage Accurate: 99.8% → 99.8%

Time: 3.2s

Alternatives: 5

Speedup: 1.1×

• 67.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]

FPCore

(FPCore (x)
  :precision binary64
  :pre TRUE
  (* (* x x) (- 3.0 (* x 2.0))))

C

double code(double x) {
	return (x * x) * (3.0 - (x * 2.0));
}

Fortran

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = (x * x) * (3.0d0 - (x * 2.0d0))
end function

Java

public static double code(double x) {
	return (x * x) * (3.0 - (x * 2.0));
}

Python

def code(x):
	return (x * x) * (3.0 - (x * 2.0))

Julia

function code(x)
	return Float64(Float64(x * x) * Float64(3.0 - Float64(x * 2.0)))
end

MATLAB

function tmp = code(x)
	tmp = (x * x) * (3.0 - (x * 2.0));
end

Wolfram

code[x_] := N[(N[(x * x), $MachinePrecision] * N[(3.0 - N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x):
	x in [-inf, +inf]
code: THEORY
BEGIN
f(x: real): real =
	(x * x) * ((3) - (x * (2)))
END code

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]

FPCore

(FPCore (x)
  :precision binary64
  :pre TRUE
  (* (* x x) (- 3.0 (* x 2.0))))

C

double code(double x) {
	return (x * x) * (3.0 - (x * 2.0));
}

Fortran

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = (x * x) * (3.0d0 - (x * 2.0d0))
end function

Java

public static double code(double x) {
	return (x * x) * (3.0 - (x * 2.0));
}

Python

def code(x):
	return (x * x) * (3.0 - (x * 2.0))

Julia

function code(x)
	return Float64(Float64(x * x) * Float64(3.0 - Float64(x * 2.0)))
end

MATLAB

function tmp = code(x)
	tmp = (x * x) * (3.0 - (x * 2.0));
end

Wolfram

code[x_] := N[(N[(x * x), $MachinePrecision] * N[(3.0 - N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x):
	x in [-inf, +inf]
code: THEORY
BEGIN
f(x: real): real =
	(x * x) * ((3) - (x * (2)))
END code

Alternative 1: 99.8% accurate, 1.1× speedup

Math

\[x \cdot \left(\mathsf{fma}\left(-2, x, 3\right) \cdot x\right) \]

FPCore

(FPCore (x)
  :precision binary64
  :pre TRUE
  (* x (* (fma -2.0 x 3.0) x)))

C

double code(double x) {
	return x * (fma(-2.0, x, 3.0) * x);
}

Julia

function code(x)
	return Float64(x * Float64(fma(-2.0, x, 3.0) * x))
end

Wolfram

code[x_] := N[(x * N[(N[(-2.0 * x + 3.0), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x):
	x in [-inf, +inf]
code: THEORY
BEGIN
f(x: real): real =
	x * ((((-2) * x) + (3)) * x)
END code

Derivation

1. Initial program 99.8%

   \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]
2. Step-by-step derivation

3. Applied rewrites 99.8%

   \[\leadsto x \cdot \left(\mathsf{fma}\left(-2, x, 3\right) \cdot x\right) \]
4. Add Preprocessing

Alternative 2: 97.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\\ t_1 := \left(x \cdot x\right) \cdot \left(-2 \cdot x\right)\\ \mathbf{if}\;t\_0 \leq -400000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 4 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{\frac{1}{3 \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* (* x x) (- 3.0 (* x 2.0))))
       (t_1 (* (* x x) (* -2.0 x))))
  (if (<= t_0 -400000000.0)
    t_1
    (if (<= t_0 4e-10) (/ x (/ 1.0 (* 3.0 x))) t_1))))

C

double code(double x) {
	double t_0 = (x * x) * (3.0 - (x * 2.0));
	double t_1 = (x * x) * (-2.0 * x);
	double tmp;
	if (t_0 <= -400000000.0) {
		tmp = t_1;
	} else if (t_0 <= 4e-10) {
		tmp = x / (1.0 / (3.0 * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x * x) * (3.0d0 - (x * 2.0d0))
    t_1 = (x * x) * ((-2.0d0) * x)
    if (t_0 <= (-400000000.0d0)) then
        tmp = t_1
    else if (t_0 <= 4d-10) then
        tmp = x / (1.0d0 / (3.0d0 * x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = (x * x) * (3.0 - (x * 2.0));
	double t_1 = (x * x) * (-2.0 * x);
	double tmp;
	if (t_0 <= -400000000.0) {
		tmp = t_1;
	} else if (t_0 <= 4e-10) {
		tmp = x / (1.0 / (3.0 * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x):
	t_0 = (x * x) * (3.0 - (x * 2.0))
	t_1 = (x * x) * (-2.0 * x)
	tmp = 0
	if t_0 <= -400000000.0:
		tmp = t_1
	elif t_0 <= 4e-10:
		tmp = x / (1.0 / (3.0 * x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x)
	t_0 = Float64(Float64(x * x) * Float64(3.0 - Float64(x * 2.0)))
	t_1 = Float64(Float64(x * x) * Float64(-2.0 * x))
	tmp = 0.0
	if (t_0 <= -400000000.0)
		tmp = t_1;
	elseif (t_0 <= 4e-10)
		tmp = Float64(x / Float64(1.0 / Float64(3.0 * x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = (x * x) * (3.0 - (x * 2.0));
	t_1 = (x * x) * (-2.0 * x);
	tmp = 0.0;
	if (t_0 <= -400000000.0)
		tmp = t_1;
	elseif (t_0 <= 4e-10)
		tmp = x / (1.0 / (3.0 * x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(x * x), $MachinePrecision] * N[(3.0 - N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] * N[(-2.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -400000000.0], t$95$1, If[LessEqual[t$95$0, 4e-10], N[(x / N[(1.0 / N[(3.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

ReFlow

f(x):
	x in [-inf, +inf]
code: THEORY
BEGIN
f(x: real): real =
	LET t_0 = ((x * x) * ((3) - (x * (2)))) IN
		LET t_1 = ((x * x) * ((-2) * x)) IN
			LET tmp_1 = IF (t_0 <= (400000000000000014572878926199096631666218826239855843596160411834716796875e-84)) THEN (x / ((1) / ((3) * x))) ELSE t_1 ENDIF IN
			LET tmp = IF (t_0 <= (-4e8)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x x) (-.f64 #s(literal 3 binary64) (*.f64 x #s(literal 2 binary64)))) < -4e8 or 4.0000000000000001e-10 < (*.f64 (*.f64 x x) (-.f64 #s(literal 3 binary64) (*.f64 x #s(literal 2 binary64))))

   1. Initial program 99.8%

      \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot x\right) \cdot \left(-2 \cdot x\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.2%

      \[\leadsto \left(x \cdot x\right) \cdot \left(-2 \cdot x\right) \]

   if -4e8 < (*.f64 (*.f64 x x) (-.f64 #s(literal 3 binary64) (*.f64 x #s(literal 2 binary64)))) < 4.0000000000000001e-10

   1. Initial program 99.8%

      \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 99.8%

      \[\leadsto \left(x \cdot x\right) \cdot \left(\left(3 - x\right) - x\right) \]
   4. Step-by-step derivation

   5. Applied rewrites 99.8%

      \[\leadsto \frac{x}{\frac{1}{\mathsf{fma}\left(-2, x, 3\right) \cdot x}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{x}{\frac{1}{3 \cdot x}} \]
   7. Step-by-step derivation

   8. Applied rewrites 62.0%

      \[\leadsto \frac{x}{\frac{1}{3 \cdot x}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 97.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\\ t_1 := \left(x \cdot x\right) \cdot \left(-2 \cdot x\right)\\ \mathbf{if}\;t\_0 \leq -400000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 4 \cdot 10^{-10}:\\ \;\;\;\;\left(x \cdot x\right) \cdot 3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* (* x x) (- 3.0 (* x 2.0))))
       (t_1 (* (* x x) (* -2.0 x))))
  (if (<= t_0 -400000000.0)
    t_1
    (if (<= t_0 4e-10) (* (* x x) 3.0) t_1))))

C

double code(double x) {
	double t_0 = (x * x) * (3.0 - (x * 2.0));
	double t_1 = (x * x) * (-2.0 * x);
	double tmp;
	if (t_0 <= -400000000.0) {
		tmp = t_1;
	} else if (t_0 <= 4e-10) {
		tmp = (x * x) * 3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x * x) * (3.0d0 - (x * 2.0d0))
    t_1 = (x * x) * ((-2.0d0) * x)
    if (t_0 <= (-400000000.0d0)) then
        tmp = t_1
    else if (t_0 <= 4d-10) then
        tmp = (x * x) * 3.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = (x * x) * (3.0 - (x * 2.0));
	double t_1 = (x * x) * (-2.0 * x);
	double tmp;
	if (t_0 <= -400000000.0) {
		tmp = t_1;
	} else if (t_0 <= 4e-10) {
		tmp = (x * x) * 3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x):
	t_0 = (x * x) * (3.0 - (x * 2.0))
	t_1 = (x * x) * (-2.0 * x)
	tmp = 0
	if t_0 <= -400000000.0:
		tmp = t_1
	elif t_0 <= 4e-10:
		tmp = (x * x) * 3.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x)
	t_0 = Float64(Float64(x * x) * Float64(3.0 - Float64(x * 2.0)))
	t_1 = Float64(Float64(x * x) * Float64(-2.0 * x))
	tmp = 0.0
	if (t_0 <= -400000000.0)
		tmp = t_1;
	elseif (t_0 <= 4e-10)
		tmp = Float64(Float64(x * x) * 3.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = (x * x) * (3.0 - (x * 2.0));
	t_1 = (x * x) * (-2.0 * x);
	tmp = 0.0;
	if (t_0 <= -400000000.0)
		tmp = t_1;
	elseif (t_0 <= 4e-10)
		tmp = (x * x) * 3.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(x * x), $MachinePrecision] * N[(3.0 - N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] * N[(-2.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -400000000.0], t$95$1, If[LessEqual[t$95$0, 4e-10], N[(N[(x * x), $MachinePrecision] * 3.0), $MachinePrecision], t$95$1]]]]

ReFlow

f(x):
	x in [-inf, +inf]
code: THEORY
BEGIN
f(x: real): real =
	LET t_0 = ((x * x) * ((3) - (x * (2)))) IN
		LET t_1 = ((x * x) * ((-2) * x)) IN
			LET tmp_1 = IF (t_0 <= (400000000000000014572878926199096631666218826239855843596160411834716796875e-84)) THEN ((x * x) * (3)) ELSE t_1 ENDIF IN
			LET tmp = IF (t_0 <= (-4e8)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x x) (-.f64 #s(literal 3 binary64) (*.f64 x #s(literal 2 binary64)))) < -4e8 or 4.0000000000000001e-10 < (*.f64 (*.f64 x x) (-.f64 #s(literal 3 binary64) (*.f64 x #s(literal 2 binary64))))

   1. Initial program 99.8%

      \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot x\right) \cdot \left(-2 \cdot x\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 75.2%

      \[\leadsto \left(x \cdot x\right) \cdot \left(-2 \cdot x\right) \]

   if -4e8 < (*.f64 (*.f64 x x) (-.f64 #s(literal 3 binary64) (*.f64 x #s(literal 2 binary64)))) < 4.0000000000000001e-10

   1. Initial program 99.8%

      \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(x \cdot x\right) \cdot 3 \]
   3. Step-by-step derivation

   4. Applied rewrites 62.0%

      \[\leadsto \left(x \cdot x\right) \cdot 3 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 62.0% accurate, 1.8× speedup

Math

\[\left(x \cdot x\right) \cdot 3 \]

FPCore

(FPCore (x)
  :precision binary64
  :pre TRUE
  (* (* x x) 3.0))

C

double code(double x) {
	return (x * x) * 3.0;
}

Fortran

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = (x * x) * 3.0d0
end function

Java

public static double code(double x) {
	return (x * x) * 3.0;
}

Python

def code(x):
	return (x * x) * 3.0

Julia

function code(x)
	return Float64(Float64(x * x) * 3.0)
end

MATLAB

function tmp = code(x)
	tmp = (x * x) * 3.0;
end

Wolfram

code[x_] := N[(N[(x * x), $MachinePrecision] * 3.0), $MachinePrecision]

ReFlow

f(x):
	x in [-inf, +inf]
code: THEORY
BEGIN
f(x: real): real =
	(x * x) * (3)
END code

Derivation

1. Initial program 99.8%

   \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]

2. Taylor expanded in x around 0

   \[\leadsto \left(x \cdot x\right) \cdot 3 \]
3. Step-by-step derivation

4. Applied rewrites 62.0%

   \[\leadsto \left(x \cdot x\right) \cdot 3 \]
5. Add Preprocessing

Alternative 5: 62.0% accurate, 1.8× speedup

Math

\[x \cdot \left(3 \cdot x\right) \]

FPCore

(FPCore (x)
  :precision binary64
  :pre TRUE
  (* x (* 3.0 x)))

C

double code(double x) {
	return x * (3.0 * x);
}

Fortran

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = x * (3.0d0 * x)
end function

Java

public static double code(double x) {
	return x * (3.0 * x);
}

Python

def code(x):
	return x * (3.0 * x)

Julia

function code(x)
	return Float64(x * Float64(3.0 * x))
end

MATLAB

function tmp = code(x)
	tmp = x * (3.0 * x);
end

Wolfram

code[x_] := N[(x * N[(3.0 * x), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x):
	x in [-inf, +inf]
code: THEORY
BEGIN
f(x: real): real =
	x * ((3) * x)
END code

Derivation

1. Initial program 99.8%

   \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]

2. Taylor expanded in x around 0

   \[\leadsto \left(x \cdot x\right) \cdot 3 \]
3. Step-by-step derivation

4. Applied rewrites 62.0%

   \[\leadsto \left(x \cdot x\right) \cdot 3 \]
5. Step-by-step derivation

6. Applied rewrites 62.0%

   \[\leadsto x \cdot \left(3 \cdot x\right) \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x)
  :name "Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2"
  :precision binary64
  (* (* x x) (- 3.0 (* x 2.0))))