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

Percentage Accurate: 97.9% → 100.0%

Time: 5.4s

Alternatives: 5

Speedup: 1.3×

• 21.2% 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: 97.9% 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, 1.3× speedup

Math

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

FPCore

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

C

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

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 + (y * (x - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

   \[x \cdot y + z \cdot \left(1 - y\right) \]
2. Step-by-step derivation

   1. +-commutative N/A

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

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

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

   3. *-lft-identity N/A

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

   4. associate-+l- N/A

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

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(z, \color{blue}{\left(y \cdot z - x \cdot y\right)}\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(z, \left(y \cdot z - y \cdot \color{blue}{x}\right)\right) \]

   7. distribute-lft-out-- N/A

      \[\leadsto \mathsf{\_.f64}\left(z, \left(y \cdot \color{blue}{\left(z - x\right)}\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(y, \color{blue}{\left(z - x\right)}\right)\right) \]

   9. --lowering--.f64 100.0%

      \[\leadsto \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{x}\right)\right)\right) \]

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 97.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x - z\right)\\ \mathbf{if}\;y \leq -7.3 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-24}:\\ \;\;\;\;z + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x z))))
   (if (<= y -7.3e+19) t_0 (if (<= y 4.5e-24) (+ z (* y x)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double tmp;
	if (y <= -7.3e+19) {
		tmp = t_0;
	} else if (y <= 4.5e-24) {
		tmp = z + (y * x);
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = y * (x - z)
    if (y <= (-7.3d+19)) then
        tmp = t_0
    else if (y <= 4.5d-24) then
        tmp = z + (y * x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double tmp;
	if (y <= -7.3e+19) {
		tmp = t_0;
	} else if (y <= 4.5e-24) {
		tmp = z + (y * x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x - z)
	tmp = 0
	if y <= -7.3e+19:
		tmp = t_0
	elif y <= 4.5e-24:
		tmp = z + (y * x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x - z))
	tmp = 0.0
	if (y <= -7.3e+19)
		tmp = t_0;
	elseif (y <= 4.5e-24)
		tmp = Float64(z + Float64(y * x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x - z);
	tmp = 0.0;
	if (y <= -7.3e+19)
		tmp = t_0;
	elseif (y <= 4.5e-24)
		tmp = z + (y * x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.3e+19], t$95$0, If[LessEqual[y, 4.5e-24], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.3e19 or 4.4999999999999997e-24 < y

   1. Initial program 94.5%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   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. +-commutative N/A

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. distribute-lft-out-- N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(z - x\right)\right)}\right) \]

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(-1 \cdot z - \color{blue}{-1 \cdot x}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(-1 \cdot z + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot x\right)\right)}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(-1 \cdot z + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(-1 \cdot z + x\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(x + \color{blue}{-1 \cdot z}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(x + \left(\mathsf{neg}\left(z\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(x - \color{blue}{z}\right)\right) \]

      14. --lowering--.f64 98.7%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(x, \color{blue}{z}\right)\right) \]

   5. Simplified 98.7%

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

   if -7.3e19 < y < 4.4999999999999997e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \color{blue}{z}\right) \]
   4. Step-by-step derivation

   5. Simplified 99.4%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.3 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-24}:\\ \;\;\;\;z + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x - z\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{-31}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-42}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x z))))
   (if (<= y -1.3e-31) t_0 (if (<= y 2.6e-42) z t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double tmp;
	if (y <= -1.3e-31) {
		tmp = t_0;
	} else if (y <= 2.6e-42) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = y * (x - z)
    if (y <= (-1.3d-31)) then
        tmp = t_0
    else if (y <= 2.6d-42) then
        tmp = z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double tmp;
	if (y <= -1.3e-31) {
		tmp = t_0;
	} else if (y <= 2.6e-42) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x - z)
	tmp = 0
	if y <= -1.3e-31:
		tmp = t_0
	elif y <= 2.6e-42:
		tmp = z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x - z))
	tmp = 0.0
	if (y <= -1.3e-31)
		tmp = t_0;
	elseif (y <= 2.6e-42)
		tmp = z;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x - z);
	tmp = 0.0;
	if (y <= -1.3e-31)
		tmp = t_0;
	elseif (y <= 2.6e-42)
		tmp = z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e-31], t$95$0, If[LessEqual[y, 2.6e-42], z, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.29999999999999998e-31 or 2.6e-42 < y

   1. Initial program 94.9%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   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. +-commutative N/A

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. distribute-lft-out-- N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(z - x\right)\right)}\right) \]

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(-1 \cdot z - \color{blue}{-1 \cdot x}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(-1 \cdot z + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot x\right)\right)}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(-1 \cdot z + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(-1 \cdot z + x\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(x + \color{blue}{-1 \cdot z}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(x + \left(\mathsf{neg}\left(z\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(x - \color{blue}{z}\right)\right) \]

      14. --lowering--.f64 97.3%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(x, \color{blue}{z}\right)\right) \]

   5. Simplified 97.3%

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

   if -1.29999999999999998e-31 < y < 2.6e-42

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z} \]
   4. Step-by-step derivation

   5. Simplified 83.5%

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

Alternative 4: 62.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-32}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-41}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.2e-32) (* y x) (if (<= y 2.5e-41) z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.2e-32) {
		tmp = y * x;
	} else if (y <= 2.5e-41) {
		tmp = 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 (y <= (-2.2d-32)) then
        tmp = y * x
    else if (y <= 2.5d-41) then
        tmp = 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 (y <= -2.2e-32) {
		tmp = y * x;
	} else if (y <= 2.5e-41) {
		tmp = z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.2e-32:
		tmp = y * x
	elif y <= 2.5e-41:
		tmp = z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.2e-32)
		tmp = Float64(y * x);
	elseif (y <= 2.5e-41)
		tmp = z;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.2e-32)
		tmp = y * x;
	elseif (y <= 2.5e-41)
		tmp = z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.2e-32], N[(y * x), $MachinePrecision], If[LessEqual[y, 2.5e-41], z, N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2e-32 or 2.4999999999999998e-41 < y

   1. Initial program 94.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 61.0%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 61.0%

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

   if -2.2e-32 < y < 2.4999999999999998e-41

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z} \]
   4. Step-by-step derivation

   5. Simplified 83.5%

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

Alternative 5: 36.8% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ z \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 97.2%

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

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{z} \]
4. Step-by-step derivation

5. Simplified 40.6%

   \[\leadsto \color{blue}{z} \]
6. Add Preprocessing

Developer Target 1: 100.0% accurate, 1.3× 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 2024145 
(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))))