Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J

Average Error: 3.5 → 0.3

Time: 11.6s

Precision: binary64

Cost: 7112

Math

\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

↓

\[\begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(1 - z\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-86}:\\ \;\;\;\;x + z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(y, z, 1\right) - z\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (if (<= x -7e-19)
   (+ (* x (- 1.0 z)) (* x (* y z)))
   (if (<= x 2.3e-86) (+ x (* z (* x (+ y -1.0)))) (* x (- (fma y z 1.0) z)))))

C

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

↓

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7e-19) {
		tmp = (x * (1.0 - z)) + (x * (y * z));
	} else if (x <= 2.3e-86) {
		tmp = x + (z * (x * (y + -1.0)));
	} else {
		tmp = x * (fma(y, z, 1.0) - z);
	}
	return tmp;
}

Julia

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

↓

function code(x, y, z)
	tmp = 0.0
	if (x <= -7e-19)
		tmp = Float64(Float64(x * Float64(1.0 - z)) + Float64(x * Float64(y * z)));
	elseif (x <= 2.3e-86)
		tmp = Float64(x + Float64(z * Float64(x * Float64(y + -1.0))));
	else
		tmp = Float64(x * Float64(fma(y, z, 1.0) - z));
	end
	return tmp
end

Wolfram

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

↓

code[x_, y_, z_] := If[LessEqual[x, -7e-19], N[(N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e-86], N[(x + N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * z + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]]]

Target

Original	3.5
Target	0.2
Herbie	0.3

\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if x < -7.00000000000000031e-19

   1. Initial program 0.2

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Simplified 0.2

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

      [Start] 0.2	\[ x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
      *-commutative [=>] 0.2	\[ x \cdot \left(1 - \color{blue}{z \cdot \left(1 - y\right)}\right) \]
      sub-neg [=>] 0.2	\[ x \cdot \left(1 - z \cdot \color{blue}{\left(1 + \left(-y\right)\right)}\right) \]
      distribute-rgt-in [=>] 0.2	\[ x \cdot \left(1 - \color{blue}{\left(1 \cdot z + \left(-y\right) \cdot z\right)}\right) \]
      associate--r+ [=>] 0.2	\[ x \cdot \color{blue}{\left(\left(1 - 1 \cdot z\right) - \left(-y\right) \cdot z\right)} \]
      *-lft-identity [=>] 0.2	\[ x \cdot \left(\left(1 - \color{blue}{z}\right) - \left(-y\right) \cdot z\right) \]
      sub-neg [=>] 0.2	\[ x \cdot \left(\color{blue}{\left(1 + \left(-z\right)\right)} - \left(-y\right) \cdot z\right) \]
      distribute-lft-out-- [<=] 0.2	\[ \color{blue}{x \cdot \left(1 + \left(-z\right)\right) - x \cdot \left(\left(-y\right) \cdot z\right)} \]
      distribute-lft-in [=>] 0.2	\[ \color{blue}{\left(x \cdot 1 + x \cdot \left(-z\right)\right)} - x \cdot \left(\left(-y\right) \cdot z\right) \]
      *-rgt-identity [=>] 0.2	\[ \left(\color{blue}{x} + x \cdot \left(-z\right)\right) - x \cdot \left(\left(-y\right) \cdot z\right) \]
      +-commutative [=>] 0.2	\[ \color{blue}{\left(x \cdot \left(-z\right) + x\right)} - x \cdot \left(\left(-y\right) \cdot z\right) \]
      associate-+r- [<=] 0.2	\[ \color{blue}{x \cdot \left(-z\right) + \left(x - x \cdot \left(\left(-y\right) \cdot z\right)\right)} \]
      *-commutative [=>] 0.2	\[ x \cdot \left(-z\right) + \left(x - \color{blue}{\left(\left(-y\right) \cdot z\right) \cdot x}\right) \]
      cancel-sign-sub-inv [=>] 0.2	\[ x \cdot \left(-z\right) + \color{blue}{\left(x + \left(-\left(-y\right) \cdot z\right) \cdot x\right)} \]
      distribute-rgt-neg-in [=>] 0.2	\[ x \cdot \left(-z\right) + \left(x + \color{blue}{\left(\left(-y\right) \cdot \left(-z\right)\right)} \cdot x\right) \]
      distribute-rgt1-in [=>] 0.2	\[ x \cdot \left(-z\right) + \color{blue}{\left(\left(-y\right) \cdot \left(-z\right) + 1\right) \cdot x} \]
      *-commutative [=>] 0.2	\[ x \cdot \left(-z\right) + \color{blue}{x \cdot \left(\left(-y\right) \cdot \left(-z\right) + 1\right)} \]
      +-commutative [=>] 0.2	\[ \color{blue}{x \cdot \left(\left(-y\right) \cdot \left(-z\right) + 1\right) + x \cdot \left(-z\right)} \]

   3. Applied egg-rr 0.2

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

   if -7.00000000000000031e-19 < x < 2.29999999999999996e-86

   1. Initial program 6.3

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Simplified 6.3

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

      [Start] 6.3	\[ x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
      *-commutative [=>] 6.3	\[ x \cdot \left(1 - \color{blue}{z \cdot \left(1 - y\right)}\right) \]
      sub-neg [=>] 6.3	\[ x \cdot \left(1 - z \cdot \color{blue}{\left(1 + \left(-y\right)\right)}\right) \]
      distribute-rgt-in [=>] 6.3	\[ x \cdot \left(1 - \color{blue}{\left(1 \cdot z + \left(-y\right) \cdot z\right)}\right) \]
      associate--r+ [=>] 6.3	\[ x \cdot \color{blue}{\left(\left(1 - 1 \cdot z\right) - \left(-y\right) \cdot z\right)} \]
      *-lft-identity [=>] 6.3	\[ x \cdot \left(\left(1 - \color{blue}{z}\right) - \left(-y\right) \cdot z\right) \]
      sub-neg [=>] 6.3	\[ x \cdot \left(\color{blue}{\left(1 + \left(-z\right)\right)} - \left(-y\right) \cdot z\right) \]
      distribute-lft-out-- [<=] 6.3	\[ \color{blue}{x \cdot \left(1 + \left(-z\right)\right) - x \cdot \left(\left(-y\right) \cdot z\right)} \]
      distribute-lft-in [=>] 6.3	\[ \color{blue}{\left(x \cdot 1 + x \cdot \left(-z\right)\right)} - x \cdot \left(\left(-y\right) \cdot z\right) \]
      *-rgt-identity [=>] 6.3	\[ \left(\color{blue}{x} + x \cdot \left(-z\right)\right) - x \cdot \left(\left(-y\right) \cdot z\right) \]
      +-commutative [=>] 6.3	\[ \color{blue}{\left(x \cdot \left(-z\right) + x\right)} - x \cdot \left(\left(-y\right) \cdot z\right) \]
      associate-+r- [<=] 6.3	\[ \color{blue}{x \cdot \left(-z\right) + \left(x - x \cdot \left(\left(-y\right) \cdot z\right)\right)} \]
      *-commutative [=>] 6.3	\[ x \cdot \left(-z\right) + \left(x - \color{blue}{\left(\left(-y\right) \cdot z\right) \cdot x}\right) \]
      cancel-sign-sub-inv [=>] 6.3	\[ x \cdot \left(-z\right) + \color{blue}{\left(x + \left(-\left(-y\right) \cdot z\right) \cdot x\right)} \]
      distribute-rgt-neg-in [=>] 6.3	\[ x \cdot \left(-z\right) + \left(x + \color{blue}{\left(\left(-y\right) \cdot \left(-z\right)\right)} \cdot x\right) \]
      distribute-rgt1-in [=>] 6.3	\[ x \cdot \left(-z\right) + \color{blue}{\left(\left(-y\right) \cdot \left(-z\right) + 1\right) \cdot x} \]
      *-commutative [=>] 6.3	\[ x \cdot \left(-z\right) + \color{blue}{x \cdot \left(\left(-y\right) \cdot \left(-z\right) + 1\right)} \]
      +-commutative [=>] 6.3	\[ \color{blue}{x \cdot \left(\left(-y\right) \cdot \left(-z\right) + 1\right) + x \cdot \left(-z\right)} \]

   3. Taylor expanded in z around -inf 3.0

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

   4. Simplified 0.1

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

      [Start] 3.0	\[ -1 \cdot \left(\left(1 + -1 \cdot y\right) \cdot \left(z \cdot x\right)\right) + x \]
      +-commutative [=>] 3.0	\[ \color{blue}{x + -1 \cdot \left(\left(1 + -1 \cdot y\right) \cdot \left(z \cdot x\right)\right)} \]
      mul-1-neg [=>] 3.0	\[ x + \color{blue}{\left(-\left(1 + -1 \cdot y\right) \cdot \left(z \cdot x\right)\right)} \]
      unsub-neg [=>] 3.0	\[ \color{blue}{x - \left(1 + -1 \cdot y\right) \cdot \left(z \cdot x\right)} \]
      associate-*r* [=>] 6.3	\[ x - \color{blue}{\left(\left(1 + -1 \cdot y\right) \cdot z\right) \cdot x} \]
      *-commutative [=>] 6.3	\[ x - \color{blue}{\left(z \cdot \left(1 + -1 \cdot y\right)\right)} \cdot x \]
      associate-*l* [=>] 0.1	\[ x - \color{blue}{z \cdot \left(\left(1 + -1 \cdot y\right) \cdot x\right)} \]
      mul-1-neg [=>] 0.1	\[ x - z \cdot \left(\left(1 + \color{blue}{\left(-y\right)}\right) \cdot x\right) \]
      unsub-neg [=>] 0.1	\[ x - z \cdot \left(\color{blue}{\left(1 - y\right)} \cdot x\right) \]

   if 2.29999999999999996e-86 < x

   1. Initial program 0.8

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Simplified 0.8

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

      [Start] 0.8	\[ x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
      *-commutative [=>] 0.8	\[ x \cdot \left(1 - \color{blue}{z \cdot \left(1 - y\right)}\right) \]
      sub-neg [=>] 0.8	\[ x \cdot \left(1 - z \cdot \color{blue}{\left(1 + \left(-y\right)\right)}\right) \]
      distribute-rgt-in [=>] 0.8	\[ x \cdot \left(1 - \color{blue}{\left(1 \cdot z + \left(-y\right) \cdot z\right)}\right) \]
      associate--r+ [=>] 0.8	\[ x \cdot \color{blue}{\left(\left(1 - 1 \cdot z\right) - \left(-y\right) \cdot z\right)} \]
      *-lft-identity [=>] 0.8	\[ x \cdot \left(\left(1 - \color{blue}{z}\right) - \left(-y\right) \cdot z\right) \]
      sub-neg [=>] 0.8	\[ x \cdot \left(\color{blue}{\left(1 + \left(-z\right)\right)} - \left(-y\right) \cdot z\right) \]
      distribute-lft-out-- [<=] 0.8	\[ \color{blue}{x \cdot \left(1 + \left(-z\right)\right) - x \cdot \left(\left(-y\right) \cdot z\right)} \]
      distribute-lft-in [=>] 0.8	\[ \color{blue}{\left(x \cdot 1 + x \cdot \left(-z\right)\right)} - x \cdot \left(\left(-y\right) \cdot z\right) \]
      *-rgt-identity [=>] 0.8	\[ \left(\color{blue}{x} + x \cdot \left(-z\right)\right) - x \cdot \left(\left(-y\right) \cdot z\right) \]
      +-commutative [=>] 0.8	\[ \color{blue}{\left(x \cdot \left(-z\right) + x\right)} - x \cdot \left(\left(-y\right) \cdot z\right) \]
      associate-+r- [<=] 0.8	\[ \color{blue}{x \cdot \left(-z\right) + \left(x - x \cdot \left(\left(-y\right) \cdot z\right)\right)} \]
      *-commutative [=>] 0.8	\[ x \cdot \left(-z\right) + \left(x - \color{blue}{\left(\left(-y\right) \cdot z\right) \cdot x}\right) \]
      cancel-sign-sub-inv [=>] 0.8	\[ x \cdot \left(-z\right) + \color{blue}{\left(x + \left(-\left(-y\right) \cdot z\right) \cdot x\right)} \]
      distribute-rgt-neg-in [=>] 0.8	\[ x \cdot \left(-z\right) + \left(x + \color{blue}{\left(\left(-y\right) \cdot \left(-z\right)\right)} \cdot x\right) \]
      distribute-rgt1-in [=>] 0.8	\[ x \cdot \left(-z\right) + \color{blue}{\left(\left(-y\right) \cdot \left(-z\right) + 1\right) \cdot x} \]
      *-commutative [=>] 0.8	\[ x \cdot \left(-z\right) + \color{blue}{x \cdot \left(\left(-y\right) \cdot \left(-z\right) + 1\right)} \]
      +-commutative [=>] 0.8	\[ \color{blue}{x \cdot \left(\left(-y\right) \cdot \left(-z\right) + 1\right) + x \cdot \left(-z\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 0.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(1 - z\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-86}:\\ \;\;\;\;x + z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(y, z, 1\right) - z\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	0.3
Cost	1352

\[\begin{array}{l} t_0 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{+286}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 2
Error	12.4
Cost	1115

\[\begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+171} \lor \neg \left(y \leq -2.9 \cdot 10^{+69} \lor \neg \left(y \leq -1.6 \cdot 10^{+42}\right) \land \left(y \leq 60000000000 \lor \neg \left(y \leq 6 \cdot 10^{+58}\right) \land y \leq 2.1 \cdot 10^{+110}\right)\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 3
Error	12.7
Cost	1112

\[\begin{array}{l} t_0 := y \cdot \left(x \cdot z\right)\\ t_1 := x \cdot \left(1 - z\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+171}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+42}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.0125:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	20.5
Cost	1048

\[\begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+60}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -620000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-227}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	0.2
Cost	969

\[\begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-19} \lor \neg \left(x \leq 2 \cdot 10^{-52}\right):\\ \;\;\;\;x \cdot \left(1 - z\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 6
Error	21.3
Cost	916

\[\begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+61}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-64}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-227}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	0.3
Cost	841

\[\begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+50} \lor \neg \left(x \leq 10^{-86}\right):\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 8
Error	20.4
Cost	784

\[\begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-227}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 9
Error	4.3
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \]

Alternative 10
Error	0.9
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -0.99 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \]

Alternative 11
Error	0.9
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -0.98 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 12
Error	19.0
Cost	521

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Error	32.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023031 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :herbie-target
  (if (< (* x (- 1.0 (* (- 1.0 y) z))) -1.618195973607049e+50) (+ x (* (- 1.0 y) (* (- z) x))) (if (< (* x (- 1.0 (* (- 1.0 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1.0 y) (* (- z) x)))))

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