Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3

Percentage Accurate: 98.0% → 100.0%

Time: 4.9s

Alternatives: 6

Speedup: 1.7×

• 20.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot y + z \cdot \left(1 - y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x y) (* z (- 1.0 y))))

C

double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * y) + (z * (1.0d0 - y))
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - y));
}

Python

def code(x, y, z):
	return (x * y) + (z * (1.0 - y))

Julia

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(z * Float64(1.0 - y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) + (z * (1.0 - y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot y + z \cdot \left(1 - y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x y) (* z (- 1.0 y))))

C

double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * y) + (z * (1.0d0 - y))
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - y));
}

Python

def code(x, y, z):
	return (x * y) + (z * (1.0 - y))

Julia

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(z * Float64(1.0 - y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) + (z * (1.0 - y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x - z, y, z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (- x z) y z))

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.8%

   \[x \cdot y + z \cdot \left(1 - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

   1. distribute-rgt-out-- N/A

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

   2. unsub-neg N/A

      \[\leadsto x \cdot y + \color{blue}{\left(1 \cdot z + \left(\mathsf{neg}\left(y \cdot z\right)\right)\right)} \]

   3. mul-1-neg N/A

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

   4. *-lft-identity N/A

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

   5. +-commutative N/A

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

   6. associate-+l+ N/A

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

   7. +-commutative N/A

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

   8. mul-1-neg N/A

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

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

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

   10. mul-1-neg N/A

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

   11. *-commutative N/A

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

   12. distribute-lft-in N/A

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

   13. +-commutative N/A

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

   14. remove-double-neg N/A

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

   15. mul-1-neg N/A

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

   16. mul-1-neg N/A

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

   17. distribute-neg-in N/A

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

   18. +-commutative N/A

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

   19. *-commutative N/A

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

   20. lower-fma.f64 N/A

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

5. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x - z, y, z\right)} \]
6. Add Preprocessing

Alternative 2: 60.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+207}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \mathbf{elif}\;y \leq -1.62 \cdot 10^{-100} \lor \neg \left(y \leq 2.5 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.05e+207)
   (* (- z) y)
   (if (or (<= y -1.62e-100) (not (<= y 2.5e-12))) (* y x) (* 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.05e+207) {
		tmp = -z * y;
	} else if ((y <= -1.62e-100) || !(y <= 2.5e-12)) {
		tmp = y * x;
	} else {
		tmp = 1.0 * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.05d+207)) then
        tmp = -z * y
    else if ((y <= (-1.62d-100)) .or. (.not. (y <= 2.5d-12))) then
        tmp = y * x
    else
        tmp = 1.0d0 * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.05e+207) {
		tmp = -z * y;
	} else if ((y <= -1.62e-100) || !(y <= 2.5e-12)) {
		tmp = y * x;
	} else {
		tmp = 1.0 * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.05e+207:
		tmp = -z * y
	elif (y <= -1.62e-100) or not (y <= 2.5e-12):
		tmp = y * x
	else:
		tmp = 1.0 * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.05e+207)
		tmp = Float64(Float64(-z) * y);
	elseif ((y <= -1.62e-100) || !(y <= 2.5e-12))
		tmp = Float64(y * x);
	else
		tmp = Float64(1.0 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.05e+207)
		tmp = -z * y;
	elseif ((y <= -1.62e-100) || ~((y <= 2.5e-12)))
		tmp = y * x;
	else
		tmp = 1.0 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.05e+207], N[((-z) * y), $MachinePrecision], If[Or[LessEqual[y, -1.62e-100], N[Not[LessEqual[y, 2.5e-12]], $MachinePrecision]], N[(y * x), $MachinePrecision], N[(1.0 * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.05e207

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. remove-double-neg N/A

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

      2. mul-1-neg N/A

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

      3. mul-1-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. unsub-neg N/A

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

      13. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 82.8%

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

   if -2.05e207 < y < -1.6200000000000001e-100 or 2.49999999999999985e-12 < y

   1. Initial program 97.7%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 45.8

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

   5. Applied rewrites 45.8%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 58.4

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

   8. Applied rewrites 58.4%

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

   if -1.6200000000000001e-100 < y < 2.49999999999999985e-12

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 80.7

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

   5. Applied rewrites 80.7%

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

   6. Taylor expanded in y around 0

      \[\leadsto 1 \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 80.5%

      \[\leadsto 1 \cdot z \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+207}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \mathbf{elif}\;y \leq -1.62 \cdot 10^{-100} \lor \neg \left(y \leq 2.5 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-103} \lor \neg \left(y \leq 2.5 \cdot 10^{-12}\right):\\ \;\;\;\;\left(x - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8.8e-103) (not (<= y 2.5e-12))) (* (- x z) y) (* (- 1.0 y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.8e-103) || !(y <= 2.5e-12)) {
		tmp = (x - z) * y;
	} else {
		tmp = (1.0 - y) * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-8.8d-103)) .or. (.not. (y <= 2.5d-12))) then
        tmp = (x - z) * y
    else
        tmp = (1.0d0 - y) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.8e-103) || !(y <= 2.5e-12)) {
		tmp = (x - z) * y;
	} else {
		tmp = (1.0 - y) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8.8e-103) or not (y <= 2.5e-12):
		tmp = (x - z) * y
	else:
		tmp = (1.0 - y) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8.8e-103) || !(y <= 2.5e-12))
		tmp = Float64(Float64(x - z) * y);
	else
		tmp = Float64(Float64(1.0 - y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -8.8e-103) || ~((y <= 2.5e-12)))
		tmp = (x - z) * y;
	else
		tmp = (1.0 - y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8.8e-103], N[Not[LessEqual[y, 2.5e-12]], $MachinePrecision]], N[(N[(x - z), $MachinePrecision] * y), $MachinePrecision], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.7999999999999997e-103 or 2.49999999999999985e-12 < y

   1. Initial program 98.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. remove-double-neg N/A

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

      2. mul-1-neg N/A

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

      3. mul-1-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. unsub-neg N/A

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

      13. lower--.f64 94.0

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

   5. Applied rewrites 94.0%

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

   if -8.7999999999999997e-103 < y < 2.49999999999999985e-12

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 80.7

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

   5. Applied rewrites 80.7%

      \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-103} \lor \neg \left(y \leq 2.5 \cdot 10^{-12}\right):\\ \;\;\;\;\left(x - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-197} \lor \neg \left(z \leq 5.5 \cdot 10^{-96}\right):\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.5e-197) (not (<= z 5.5e-96))) (* (- 1.0 y) z) (* y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e-197) || !(z <= 5.5e-96)) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-4.5d-197)) .or. (.not. (z <= 5.5d-96))) then
        tmp = (1.0d0 - y) * z
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e-197) || !(z <= 5.5e-96)) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.5e-197) or not (z <= 5.5e-96):
		tmp = (1.0 - y) * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.5e-197) || !(z <= 5.5e-96))
		tmp = Float64(Float64(1.0 - y) * z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.5e-197) || ~((z <= 5.5e-96)))
		tmp = (1.0 - y) * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.5e-197], N[Not[LessEqual[z, 5.5e-96]], $MachinePrecision]], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], N[(y * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5000000000000001e-197 or 5.4999999999999997e-96 < z

   1. Initial program 98.4%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.1

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

   5. Applied rewrites 79.1%

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

   if -4.5000000000000001e-197 < z < 5.4999999999999997e-96

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 18.6

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

   5. Applied rewrites 18.6%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 83.6

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

   8. Applied rewrites 83.6%

      \[\leadsto \color{blue}{y \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-197} \lor \neg \left(z \leq 5.5 \cdot 10^{-96}\right):\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.62 \cdot 10^{-100} \lor \neg \left(y \leq 2.5 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.62e-100) (not (<= y 2.5e-12))) (* y x) (* 1.0 z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.62e-100) || !(y <= 2.5e-12)) {
		tmp = y * x;
	} else {
		tmp = 1.0 * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.62d-100)) .or. (.not. (y <= 2.5d-12))) then
        tmp = y * x
    else
        tmp = 1.0d0 * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.62e-100) || !(y <= 2.5e-12)) {
		tmp = y * x;
	} else {
		tmp = 1.0 * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.62e-100) or not (y <= 2.5e-12):
		tmp = y * x
	else:
		tmp = 1.0 * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.62e-100) || !(y <= 2.5e-12))
		tmp = Float64(y * x);
	else
		tmp = Float64(1.0 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.62e-100) || ~((y <= 2.5e-12)))
		tmp = y * x;
	else
		tmp = 1.0 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.62e-100], N[Not[LessEqual[y, 2.5e-12]], $MachinePrecision]], N[(y * x), $MachinePrecision], N[(1.0 * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6200000000000001e-100 or 2.49999999999999985e-12 < y

   1. Initial program 98.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 49.9

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

   5. Applied rewrites 49.9%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 56.2

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

   8. Applied rewrites 56.2%

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

   if -1.6200000000000001e-100 < y < 2.49999999999999985e-12

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 80.7

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

   5. Applied rewrites 80.7%

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

   6. Taylor expanded in y around 0

      \[\leadsto 1 \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 80.5%

      \[\leadsto 1 \cdot z \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.62 \cdot 10^{-100} \lor \neg \left(y \leq 2.5 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 42.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ y \cdot x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* y x))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

   \[x \cdot y + z \cdot \left(1 - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 62.3

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

5. Applied rewrites 62.3%

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

6. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 42.5

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

8. Applied rewrites 42.5%

   \[\leadsto \color{blue}{y \cdot x} \]
9. Add Preprocessing

Developer Target 1: 100.0% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024323 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- z (* (- z x) y)))

  (+ (* x y) (* z (- 1.0 y))))