Linear.V3:cross from linear-1.19.1.3

Percentage Accurate: 99.2% → 99.6%

Time: 1.8s

Alternatives: 4

Speedup: 1.0×

• 77.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[x \cdot y - z \cdot t \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (x * y) - (z * 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 * t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.2% accurate, 1.0× speedup

Math

\[x \cdot y - z \cdot t \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (x * y) - (z * 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 * t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.2%

   \[x \cdot y - z \cdot t \]
2. Step-by-step derivation

3. Applied rewrites 99.6%

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

Alternative 2: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \left(-z\right) \cdot t\\ \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 50000000000000:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* (- z) t)))
  (if (<= (* z t) -2e-20)
    t_1
    (if (<= (* z t) 50000000000000.0) (* x y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -z * t;
	double tmp;
	if ((z * t) <= -2e-20) {
		tmp = t_1;
	} else if ((z * t) <= 50000000000000.0) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -z * t
    if ((z * t) <= (-2d-20)) then
        tmp = t_1
    else if ((z * t) <= 50000000000000.0d0) then
        tmp = x * y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -z * t;
	double tmp;
	if ((z * t) <= -2e-20) {
		tmp = t_1;
	} else if ((z * t) <= 50000000000000.0) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -z * t
	tmp = 0
	if (z * t) <= -2e-20:
		tmp = t_1
	elif (z * t) <= 50000000000000.0:
		tmp = x * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-z) * t)
	tmp = 0.0
	if (Float64(z * t) <= -2e-20)
		tmp = t_1;
	elseif (Float64(z * t) <= 50000000000000.0)
		tmp = Float64(x * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -z * t;
	tmp = 0.0;
	if ((z * t) <= -2e-20)
		tmp = t_1;
	elseif ((z * t) <= 50000000000000.0)
		tmp = x * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-z) * t), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -2e-20], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 50000000000000.0], N[(x * y), $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 = ((- z) * t) IN
		LET tmp_1 = IF ((z * t) <= (5e13)) THEN (x * y) ELSE t_1 ENDIF IN
		LET tmp = IF ((z * t) <= (-199999999999999989030654290841914330345900740557478489421543155213356612875941209495067596435546875e-118)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1.9999999999999999e-20 or 5e13 < (*.f64 z t)

   1. Initial program 99.2%

      \[x \cdot y - z \cdot t \]

   2. Taylor expanded in x around 0

      \[\leadsto -1 \cdot \left(t \cdot z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 51.9%

      \[\leadsto -1 \cdot \left(t \cdot z\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 51.9%

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

   if -1.9999999999999999e-20 < (*.f64 z t) < 5e13

   1. Initial program 99.2%

      \[x \cdot y - z \cdot t \]

   2. Taylor expanded in x around 0

      \[\leadsto -1 \cdot \left(t \cdot z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 51.9%

      \[\leadsto -1 \cdot \left(t \cdot z\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 51.9%

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

   7. Taylor expanded in x around inf

      \[\leadsto x \cdot y \]
   8. Step-by-step derivation

   9. Applied rewrites 52.0%

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

Alternative 3: 52.0% accurate, 2.4× speedup

Math

\[x \cdot y \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(x * y), $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
END code

Derivation

1. Initial program 99.2%

   \[x \cdot y - z \cdot t \]

2. Taylor expanded in x around 0

   \[\leadsto -1 \cdot \left(t \cdot z\right) \]
3. Step-by-step derivation

4. Applied rewrites 51.9%

   \[\leadsto -1 \cdot \left(t \cdot z\right) \]
5. Step-by-step derivation

6. Applied rewrites 51.9%

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

7. Taylor expanded in x around inf

   \[\leadsto x \cdot y \]
8. Step-by-step derivation

9. Applied rewrites 52.0%

   \[\leadsto x \cdot y \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))