\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t} \]

↓

\[x + \frac{-2}{\frac{1}{\frac{y}{2 \cdot z}} - \frac{t}{z}} \]

(FPCore (x y z t)
 :precision binary64
 (- x (/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t)))))

↓

(FPCore (x y z t)
 :precision binary64
 (+ x (/ -2.0 (- (/ 1.0 (/ y (* 2.0 z))) (/ t z)))))

double code(double x, double y, double z, double t) {
	return x - (((y * 2.0) * z) / (((z * 2.0) * z) - (y * t)));
}

↓

double code(double x, double y, double z, double t) {
	return x + (-2.0 / ((1.0 / (y / (2.0 * z))) - (t / z)));
}

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x - (((y * 2.0d0) * z) / (((z * 2.0d0) * z) - (y * t)))
end function

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((-2.0d0) / ((1.0d0 / (y / (2.0d0 * z))) - (t / z)))
end function

public static double code(double x, double y, double z, double t) {
	return x - (((y * 2.0) * z) / (((z * 2.0) * z) - (y * t)));
}

↓

public static double code(double x, double y, double z, double t) {
	return x + (-2.0 / ((1.0 / (y / (2.0 * z))) - (t / z)));
}

def code(x, y, z, t):
	return x - (((y * 2.0) * z) / (((z * 2.0) * z) - (y * t)))

↓

def code(x, y, z, t):
	return x + (-2.0 / ((1.0 / (y / (2.0 * z))) - (t / z)))

function code(x, y, z, t)
	return Float64(x - Float64(Float64(Float64(y * 2.0) * z) / Float64(Float64(Float64(z * 2.0) * z) - Float64(y * t))))
end

↓

function code(x, y, z, t)
	return Float64(x + Float64(-2.0 / Float64(Float64(1.0 / Float64(y / Float64(2.0 * z))) - Float64(t / z))))
end

function tmp = code(x, y, z, t)
	tmp = x - (((y * 2.0) * z) / (((z * 2.0) * z) - (y * t)));
end

↓

function tmp = code(x, y, z, t)
	tmp = x + (-2.0 / ((1.0 / (y / (2.0 * z))) - (t / z)));
end

code[x_, y_, z_, t_] := N[(x - N[(N[(N[(y * 2.0), $MachinePrecision] * z), $MachinePrecision] / N[(N[(N[(z * 2.0), $MachinePrecision] * z), $MachinePrecision] - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_] := N[(x + N[(-2.0 / N[(N[(1.0 / N[(y / N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}

↓

x + \frac{-2}{\frac{1}{\frac{y}{2 \cdot z}} - \frac{t}{z}}

Original	11.8
Target	0.1
Herbie	0.1

Derivation

Initial program 11.8
\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t} \]
Simplified0.1
\[\leadsto \color{blue}{x + \frac{-2}{2 \cdot \frac{z}{y} - \frac{t}{z}}} \]
Proof
(+.f64 x (/.f64 -2 (-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z)))): 0 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (Rewrite<= metadata-eval (neg.f64 2)) (-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z)))): 0 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (-.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 2 z) y)) (/.f64 t z)))): 0 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (-.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 z 2)) y) (/.f64 t z)))): 0 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (-.f64 (/.f64 (*.f64 z 2) y) (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 t z)))))): 0 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (-.f64 (/.f64 (*.f64 z 2) y) (*.f64 (Rewrite<= *-inverses_binary64 (/.f64 y y)) (/.f64 t z))))): 0 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (-.f64 (/.f64 (*.f64 z 2) y) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 y t) (*.f64 y z)))))): 22 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (-.f64 (/.f64 (*.f64 z 2) y) (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (*.f64 y t) z) y))))): 3 points increase in error, 18 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (Rewrite<= div-sub_binary64 (/.f64 (-.f64 (*.f64 z 2) (/.f64 (*.f64 y t) z)) y)))): 0 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (/.f64 (-.f64 (Rewrite<= /-rgt-identity_binary64 (/.f64 (*.f64 z 2) 1)) (/.f64 (*.f64 y t) z)) y))): 0 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (/.f64 (-.f64 (/.f64 (*.f64 z 2) (Rewrite<= *-inverses_binary64 (/.f64 z z))) (/.f64 (*.f64 y t) z)) y))): 0 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (/.f64 (-.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 z 2) z) z)) (/.f64 (*.f64 y t) z)) y))): 19 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (/.f64 (Rewrite<= div-sub_binary64 (/.f64 (-.f64 (*.f64 (*.f64 z 2) z) (*.f64 y t)) z)) y))): 0 points increase in error, 0 points decrease in error
(+.f64 x (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 2 (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 z 2) z) (*.f64 y t)) z) y))))): 0 points increase in error, 0 points decrease in error
(+.f64 x (neg.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 2 y) (/.f64 (-.f64 (*.f64 (*.f64 z 2) z) (*.f64 y t)) z))))): 3 points increase in error, 11 points decrease in error
(+.f64 x (neg.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 y 2)) (/.f64 (-.f64 (*.f64 (*.f64 z 2) z) (*.f64 y t)) z)))): 0 points increase in error, 0 points decrease in error
(+.f64 x (neg.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 y 2) z) (-.f64 (*.f64 (*.f64 z 2) z) (*.f64 y t)))))): 45 points increase in error, 7 points decrease in error
(Rewrite<= sub-neg_binary64 (-.f64 x (/.f64 (*.f64 (*.f64 y 2) z) (-.f64 (*.f64 (*.f64 z 2) z) (*.f64 y t))))): 0 points increase in error, 0 points decrease in error
Applied egg-rr0.1
\[\leadsto x + \frac{-2}{\color{blue}{\frac{1}{\frac{y}{2 \cdot z}}} - \frac{t}{z}} \]
Final simplification0.1
\[\leadsto x + \frac{-2}{\frac{1}{\frac{y}{2 \cdot z}} - \frac{t}{z}} \]

Alternatives

Alternative 1
Error	0.1
Cost	832

\[x + \frac{-2}{2 \cdot \frac{z}{y} - \frac{t}{z}} \]

Alternative 2
Error	6.9
Cost	712

\[\begin{array}{l} t_1 := x - \frac{y}{z}\\ \mathbf{if}\;z \leq -1.1483412482215439 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.0450506643503564 \cdot 10^{+23}:\\ \;\;\;\;x + z \cdot \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	6.9
Cost	712

\[\begin{array}{l} t_1 := x - \frac{y}{z}\\ \mathbf{if}\;z \leq -1.1483412482215439 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.0450506643503564 \cdot 10^{+23}:\\ \;\;\;\;x + 2 \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	15.8
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -2.0753880498485545 \cdot 10^{-278}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.490674323023235 \cdot 10^{-235}:\\ \;\;\;\;2 \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Error	11.6
Cost	584

\[\begin{array}{l} t_1 := x - \frac{y}{z}\\ \mathbf{if}\;z \leq -1.3747265254031916 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.551102001696844 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	16.0
Cost	64

\[x \]

Error

Try it out

Target

Derivation

Alternatives

Error

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