Radioactive exchange between two surfaces

Percentage Accurate: 85.4% → 93.1%

Time: 1.5s

Alternatives: 3

Speedup: 0.5×

• 38.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[{x}^{4} - {y}^{4} \]

FPCore

(FPCore (x y)
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))

C

double code(double x, double y) {
	return pow(x, 4.0) - pow(y, 4.0);
}

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x ** 4.0d0) - (y ** 4.0d0)
end function

Java

public static double code(double x, double y) {
	return Math.pow(x, 4.0) - Math.pow(y, 4.0);
}

Python

def code(x, y):
	return math.pow(x, 4.0) - math.pow(y, 4.0)

Julia

function code(x, y)
	return Float64((x ^ 4.0) - (y ^ 4.0))
end

MATLAB

function tmp = code(x, y)
	tmp = (x ^ 4.0) - (y ^ 4.0);
end

Wolfram

code[x_, y_] := N[(N[Power[x, 4.0], $MachinePrecision] - N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision]

Initial Program: 85.4% accurate, 1.0× speedup

Math

\[{x}^{4} - {y}^{4} \]

FPCore

(FPCore (x y)
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))

C

double code(double x, double y) {
	return pow(x, 4.0) - pow(y, 4.0);
}

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x ** 4.0d0) - (y ** 4.0d0)
end function

Java

public static double code(double x, double y) {
	return Math.pow(x, 4.0) - Math.pow(y, 4.0);
}

Python

def code(x, y):
	return math.pow(x, 4.0) - math.pow(y, 4.0)

Julia

function code(x, y)
	return Float64((x ^ 4.0) - (y ^ 4.0))
end

MATLAB

function tmp = code(x, y)
	tmp = (x ^ 4.0) - (y ^ 4.0);
end

Wolfram

code[x_, y_] := N[(N[Power[x, 4.0], $MachinePrecision] - N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision]

Alternative 1: 93.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := {x}^{4} - {y}^{4}\\ \mathbf{if}\;t\_0 \leq \infty:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-{y}^{4}\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  (let* ((t_0 (- (pow x 4.0) (pow y 4.0))))
  (if (<= t_0 INFINITY) t_0 (- (pow y 4.0)))))

C

double code(double x, double y) {
	double t_0 = pow(x, 4.0) - pow(y, 4.0);
	double tmp;
	if (t_0 <= ((double) INFINITY)) {
		tmp = t_0;
	} else {
		tmp = -pow(y, 4.0);
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double t_0 = Math.pow(x, 4.0) - Math.pow(y, 4.0);
	double tmp;
	if (t_0 <= Double.POSITIVE_INFINITY) {
		tmp = t_0;
	} else {
		tmp = -Math.pow(y, 4.0);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.pow(x, 4.0) - math.pow(y, 4.0)
	tmp = 0
	if t_0 <= math.inf:
		tmp = t_0
	else:
		tmp = -math.pow(y, 4.0)
	return tmp

Julia

function code(x, y)
	t_0 = Float64((x ^ 4.0) - (y ^ 4.0))
	tmp = 0.0
	if (t_0 <= Inf)
		tmp = t_0;
	else
		tmp = Float64(-(y ^ 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x ^ 4.0) - (y ^ 4.0);
	tmp = 0.0;
	if (t_0 <= Inf)
		tmp = t_0;
	else
		tmp = -(y ^ 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Power[x, 4.0], $MachinePrecision] - N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, Infinity], t$95$0, (-N[Power[y, 4.0], $MachinePrecision])]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) < +inf.0

   1. Initial program 85.4%

      \[{x}^{4} - {y}^{4} \]

   if +inf.0 < (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))

   1. Initial program 85.4%

      \[{x}^{4} - {y}^{4} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot {y}^{4}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{{y}^{4}} \]

      2. lower-pow.f64 58.3%

         \[\leadsto -1 \cdot {y}^{\color{blue}{4}} \]

   4. Applied rewrites 58.3%

      \[\leadsto \color{blue}{-1 \cdot {y}^{4}} \]
   5. Step-by-step derivation

      1. remove-double-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(\mathsf{neg}\left(-1 \cdot {y}^{4}\right)\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -\left(\mathsf{neg}\left(-1 \cdot {y}^{4}\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto -\left(\mathsf{neg}\left(-1 \cdot {y}^{4}\right)\right) \]

      4. distribute-lft-neg-out N/A

         \[\leadsto -\left(\mathsf{neg}\left(-1\right)\right) \cdot {y}^{4} \]

      5. metadata-eval N/A

         \[\leadsto -1 \cdot {y}^{4} \]

      6. *-lft-identity 58.3%

         \[\leadsto -{y}^{4} \]

   6. Applied rewrites 58.3%

      \[\leadsto -{y}^{4} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 92.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := {x}^{4} - {y}^{4}\\ t_1 := -{y}^{4}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-316}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq \infty:\\ \;\;\;\;{x}^{4}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  (let* ((t_0 (- (pow x 4.0) (pow y 4.0))) (t_1 (- (pow y 4.0))))
  (if (<= t_0 -1e-316) t_1 (if (<= t_0 INFINITY) (pow x 4.0) t_1))))

C

double code(double x, double y) {
	double t_0 = pow(x, 4.0) - pow(y, 4.0);
	double t_1 = -pow(y, 4.0);
	double tmp;
	if (t_0 <= -1e-316) {
		tmp = t_1;
	} else if (t_0 <= ((double) INFINITY)) {
		tmp = pow(x, 4.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double t_0 = Math.pow(x, 4.0) - Math.pow(y, 4.0);
	double t_1 = -Math.pow(y, 4.0);
	double tmp;
	if (t_0 <= -1e-316) {
		tmp = t_1;
	} else if (t_0 <= Double.POSITIVE_INFINITY) {
		tmp = Math.pow(x, 4.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.pow(x, 4.0) - math.pow(y, 4.0)
	t_1 = -math.pow(y, 4.0)
	tmp = 0
	if t_0 <= -1e-316:
		tmp = t_1
	elif t_0 <= math.inf:
		tmp = math.pow(x, 4.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64((x ^ 4.0) - (y ^ 4.0))
	t_1 = Float64(-(y ^ 4.0))
	tmp = 0.0
	if (t_0 <= -1e-316)
		tmp = t_1;
	elseif (t_0 <= Inf)
		tmp = x ^ 4.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x ^ 4.0) - (y ^ 4.0);
	t_1 = -(y ^ 4.0);
	tmp = 0.0;
	if (t_0 <= -1e-316)
		tmp = t_1;
	elseif (t_0 <= Inf)
		tmp = x ^ 4.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Power[x, 4.0], $MachinePrecision] - N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = (-N[Power[y, 4.0], $MachinePrecision])}, If[LessEqual[t$95$0, -1e-316], t$95$1, If[LessEqual[t$95$0, Infinity], N[Power[x, 4.0], $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) < -9.9999998365971443e-317 or +inf.0 < (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))

   1. Initial program 85.4%

      \[{x}^{4} - {y}^{4} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot {y}^{4}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{{y}^{4}} \]

      2. lower-pow.f64 58.3%

         \[\leadsto -1 \cdot {y}^{\color{blue}{4}} \]

   4. Applied rewrites 58.3%

      \[\leadsto \color{blue}{-1 \cdot {y}^{4}} \]
   5. Step-by-step derivation

      1. remove-double-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(\mathsf{neg}\left(-1 \cdot {y}^{4}\right)\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -\left(\mathsf{neg}\left(-1 \cdot {y}^{4}\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto -\left(\mathsf{neg}\left(-1 \cdot {y}^{4}\right)\right) \]

      4. distribute-lft-neg-out N/A

         \[\leadsto -\left(\mathsf{neg}\left(-1\right)\right) \cdot {y}^{4} \]

      5. metadata-eval N/A

         \[\leadsto -1 \cdot {y}^{4} \]

      6. *-lft-identity 58.3%

         \[\leadsto -{y}^{4} \]

   6. Applied rewrites 58.3%

      \[\leadsto -{y}^{4} \]

   if -9.9999998365971443e-317 < (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) < +inf.0

   1. Initial program 85.4%

      \[{x}^{4} - {y}^{4} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot {y}^{4}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{{y}^{4}} \]

      2. lower-pow.f64 58.3%

         \[\leadsto -1 \cdot {y}^{\color{blue}{4}} \]

   4. Applied rewrites 58.3%

      \[\leadsto \color{blue}{-1 \cdot {y}^{4}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{{x}^{4}} \]
   6. Step-by-step derivation

      1. lower-pow.f64 56.8%

         \[\leadsto {x}^{\color{blue}{4}} \]

   7. Applied rewrites 56.8%

      \[\leadsto \color{blue}{{x}^{4}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 56.8% accurate, 2.1× speedup

Math

\[{x}^{4} \]

FPCore

(FPCore (x y)
  :precision binary64
  (pow x 4.0))

C

double code(double x, double y) {
	return pow(x, 4.0);
}

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x ** 4.0d0
end function

Java

public static double code(double x, double y) {
	return Math.pow(x, 4.0);
}

Python

def code(x, y):
	return math.pow(x, 4.0)

Julia

function code(x, y)
	return x ^ 4.0
end

MATLAB

function tmp = code(x, y)
	tmp = x ^ 4.0;
end

Wolfram

code[x_, y_] := N[Power[x, 4.0], $MachinePrecision]

Derivation

1. Initial program 85.4%

   \[{x}^{4} - {y}^{4} \]

2. Taylor expanded in x around 0

   \[\leadsto \color{blue}{-1 \cdot {y}^{4}} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto -1 \cdot \color{blue}{{y}^{4}} \]

   2. lower-pow.f64 58.3%

      \[\leadsto -1 \cdot {y}^{\color{blue}{4}} \]

4. Applied rewrites 58.3%

   \[\leadsto \color{blue}{-1 \cdot {y}^{4}} \]

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{{x}^{4}} \]
6. Step-by-step derivation

   1. lower-pow.f64 56.8%

      \[\leadsto {x}^{\color{blue}{4}} \]

7. Applied rewrites 56.8%

   \[\leadsto \color{blue}{{x}^{4}} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025223 
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))