Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B

Average Accuracy: 100.0% → 100.0%

Time: 5.2s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 100.0%

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

2. Applied egg-rr 100.0%

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

   [Start] 100.0	\[ x + \left(y - x\right) \cdot z \]
   *-commutative [=>] 100.0	\[ x + \color{blue}{z \cdot \left(y - x\right)} \]
   sub-neg [=>] 100.0	\[ x + z \cdot \color{blue}{\left(y + \left(-x\right)\right)} \]
   distribute-lft-in [=>] 100.0	\[ x + \color{blue}{\left(z \cdot y + z \cdot \left(-x\right)\right)} \]
   +-commutative [=>] 100.0	\[ x + \color{blue}{\left(z \cdot \left(-x\right) + z \cdot y\right)} \]
   *-commutative [<=] 100.0	\[ x + \left(z \cdot \left(-x\right) + \color{blue}{y \cdot z}\right) \]

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	62.4%
Cost	1181

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+183}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{+95}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+33}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-12}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+83} \lor \neg \left(z \leq 3.6 \cdot 10^{+195}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 2
Accuracy	75.5%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -1.28 \cdot 10^{-138} \lor \neg \left(x \leq 4.2 \cdot 10^{-54}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 3
Accuracy	79.2%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-137} \lor \neg \left(x \leq 2.6 \cdot 10^{-50}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y - x\right)\\ \end{array} \]

Alternative 4
Accuracy	98.6%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 2.8 \cdot 10^{-12}\right):\\ \;\;\;\;z \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]

Alternative 5
Accuracy	61.1%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-137}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 10^{-29}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Accuracy	100.0%
Cost	448

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

Alternative 7
Accuracy	45.1%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023136 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))