Average Error: 0.0 → 0.0
Time: 29.4s
Precision: binary64
Cost: 7616
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
↓
\[\left(x + z \cdot \left(1 - y\right)\right) + \left(a - \mathsf{fma}\left(a, t, b \cdot \left(2 - \left(y + t\right)\right)\right)\right) \]
(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))
↓
(FPCore (x y z t a b)
 :precision binary64
 (+ (+ x (* z (- 1.0 y))) (- a (fma a t (* b (- 2.0 (+ y t)))))))
double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	return (x + (z * (1.0 - y))) + (a - fma(a, t, (b * (2.0 - (y + t)))));
}

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end
↓
function code(x, y, z, t, a, b)
	return Float64(Float64(x + Float64(z * Float64(1.0 - y))) + Float64(a - fma(a, t, Float64(b * Float64(2.0 - Float64(y + t))))))
end

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

\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b
↓
\left(x + z \cdot \left(1 - y\right)\right) + \left(a - \mathsf{fma}\left(a, t, b \cdot \left(2 - \left(y + t\right)\right)\right)\right)

Error

Derivation

  1. Initial program 0.0

    \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]
    Proof

    [Start]0.0

    \[ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

    associate-+l- [=>]0.0

    \[ \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

    sub-neg [=>]0.0

    \[ \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

    neg-sub0 [=>]0.0

    \[ \left(x - \left(y - 1\right) \cdot z\right) + \color{blue}{\left(0 - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

    associate-+r- [=>]0.0

    \[ \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) + 0\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

    +-rgt-identity [=>]0.0

    \[ \color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

    sub-neg [=>]0.0

    \[ \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

    metadata-eval [=>]0.0

    \[ \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

    sub-neg [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(\left(t - 1\right) \cdot a + \left(-\left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

    neg-mul-1 [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a + \color{blue}{-1 \cdot \left(\left(\left(y + t\right) - 2\right) \cdot b\right)}\right) \]

    metadata-eval [<=]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a + \color{blue}{\left(-1\right)} \cdot \left(\left(\left(y + t\right) - 2\right) \cdot b\right)\right) \]

    cancel-sign-sub-inv [<=]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(\left(t - 1\right) \cdot a - 1 \cdot \left(\left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

    sub-neg [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - 1 \cdot \left(\left(\left(y + t\right) - 2\right) \cdot b\right)\right) \]

    metadata-eval [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - 1 \cdot \left(\left(\left(y + t\right) - 2\right) \cdot b\right)\right) \]

    *-lft-identity [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b}\right) \]

    associate--l+ [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

  3. Taylor expanded in a around 0 0.0

    \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(\left(t - 1\right) \cdot a + -1 \cdot \left(\left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

  4. Simplified0.0

    \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(\mathsf{fma}\left(a, t, b \cdot \left(2 - \left(y + t\right)\right)\right) - a\right)} \]
    Proof

    [Start]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a + -1 \cdot \left(\left(\left(y + t\right) - 2\right) \cdot b\right)\right) \]

    sub-neg [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a + -1 \cdot \left(\left(\left(y + t\right) - 2\right) \cdot b\right)\right) \]

    metadata-eval [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a + -1 \cdot \left(\left(\left(y + t\right) - 2\right) \cdot b\right)\right) \]

    associate-*r* [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a + \color{blue}{\left(-1 \cdot \left(\left(y + t\right) - 2\right)\right) \cdot b}\right) \]

    sub-neg [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a + \left(-1 \cdot \color{blue}{\left(\left(y + t\right) + \left(-2\right)\right)}\right) \cdot b\right) \]

    +-commutative [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a + \left(-1 \cdot \left(\color{blue}{\left(t + y\right)} + \left(-2\right)\right)\right) \cdot b\right) \]

    metadata-eval [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a + \left(-1 \cdot \left(\left(t + y\right) + \color{blue}{-2}\right)\right) \cdot b\right) \]

    associate-+r+ [<=]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a + \left(-1 \cdot \color{blue}{\left(t + \left(y + -2\right)\right)}\right) \cdot b\right) \]

    neg-mul-1 [<=]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a + \color{blue}{\left(-\left(t + \left(y + -2\right)\right)\right)} \cdot b\right) \]

    cancel-sign-sub-inv [<=]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(\left(t + -1\right) \cdot a - \left(t + \left(y + -2\right)\right) \cdot b\right)} \]

    *-commutative [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{a \cdot \left(t + -1\right)} - \left(t + \left(y + -2\right)\right) \cdot b\right) \]

    distribute-rgt-out [<=]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t \cdot a + -1 \cdot a\right)} - \left(t + \left(y + -2\right)\right) \cdot b\right) \]

    +-commutative [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-1 \cdot a + t \cdot a\right)} - \left(t + \left(y + -2\right)\right) \cdot b\right) \]

    *-commutative [<=]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(-1 \cdot a + \color{blue}{a \cdot t}\right) - \left(t + \left(y + -2\right)\right) \cdot b\right) \]

    associate--l+ [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(-1 \cdot a + \left(a \cdot t - \left(t + \left(y + -2\right)\right) \cdot b\right)\right)} \]

    unsub-neg [<=]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(-1 \cdot a + \color{blue}{\left(a \cdot t + \left(-\left(t + \left(y + -2\right)\right) \cdot b\right)\right)}\right) \]

    distribute-rgt-neg-out [<=]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(-1 \cdot a + \left(a \cdot t + \color{blue}{\left(t + \left(y + -2\right)\right) \cdot \left(-b\right)}\right)\right) \]

    +-commutative [<=]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(-1 \cdot a + \color{blue}{\left(\left(t + \left(y + -2\right)\right) \cdot \left(-b\right) + a \cdot t\right)}\right) \]

    +-commutative [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(\left(\left(t + \left(y + -2\right)\right) \cdot \left(-b\right) + a \cdot t\right) + -1 \cdot a\right)} \]

    mul-1-neg [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(\left(t + \left(y + -2\right)\right) \cdot \left(-b\right) + a \cdot t\right) + \color{blue}{\left(-a\right)}\right) \]

    unsub-neg [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(\left(\left(t + \left(y + -2\right)\right) \cdot \left(-b\right) + a \cdot t\right) - a\right)} \]

    +-commutative [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(a \cdot t + \left(t + \left(y + -2\right)\right) \cdot \left(-b\right)\right)} - a\right) \]

    fma-def [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\mathsf{fma}\left(a, t, \left(t + \left(y + -2\right)\right) \cdot \left(-b\right)\right)} - a\right) \]

    distribute-rgt-neg-out [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\mathsf{fma}\left(a, t, \color{blue}{-\left(t + \left(y + -2\right)\right) \cdot b}\right) - a\right) \]

    *-commutative [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\mathsf{fma}\left(a, t, -\color{blue}{b \cdot \left(t + \left(y + -2\right)\right)}\right) - a\right) \]

    distribute-rgt-neg-in [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\mathsf{fma}\left(a, t, \color{blue}{b \cdot \left(-\left(t + \left(y + -2\right)\right)\right)}\right) - a\right) \]

    associate-+r+ [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\mathsf{fma}\left(a, t, b \cdot \left(-\color{blue}{\left(\left(t + y\right) + -2\right)}\right)\right) - a\right) \]

    +-commutative [<=]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\mathsf{fma}\left(a, t, b \cdot \left(-\left(\color{blue}{\left(y + t\right)} + -2\right)\right)\right) - a\right) \]

    distribute-neg-in [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\mathsf{fma}\left(a, t, b \cdot \color{blue}{\left(\left(-\left(y + t\right)\right) + \left(--2\right)\right)}\right) - a\right) \]

    metadata-eval [=>]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\mathsf{fma}\left(a, t, b \cdot \left(\left(-\left(y + t\right)\right) + \color{blue}{2}\right)\right) - a\right) \]

    +-commutative [<=]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\mathsf{fma}\left(a, t, b \cdot \color{blue}{\left(2 + \left(-\left(y + t\right)\right)\right)}\right) - a\right) \]

    sub-neg [<=]0.0

    \[ \left(x - \left(y + -1\right) \cdot z\right) - \left(\mathsf{fma}\left(a, t, b \cdot \color{blue}{\left(2 - \left(y + t\right)\right)}\right) - a\right) \]

  5. Final simplification0.0

    \[\leadsto \left(x + z \cdot \left(1 - y\right)\right) + \left(a - \mathsf{fma}\left(a, t, b \cdot \left(2 - \left(y + t\right)\right)\right)\right) \]

Alternatives

Alternative 1
Error35.6
Cost1904
\[\begin{array}{l} t_1 := x - a \cdot t\\ t_2 := b \cdot \left(\left(y + t\right) + -2\right)\\ t_3 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+116}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -880000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-140}:\\ \;\;\;\;x + t \cdot b\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-204}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-252}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-219}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+87}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 2
Error31.5
Cost1768
\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := x + t \cdot \left(b - a\right)\\ t_3 := b \cdot \left(\left(y + t\right) + -2\right)\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-68}:\\ \;\;\;\;x - b \cdot \left(2 - t\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-275}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-196}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-91}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-42}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+37}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 3
Error33.9
Cost1636
\[\begin{array}{l} t_1 := x - b \cdot \left(2 - t\right)\\ t_2 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-204}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-97}:\\ \;\;\;\;x - a \cdot t\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{-97}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+119}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+148}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+168}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 4
Error31.3
Cost1636
\[\begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := b \cdot \left(\left(y + t\right) + -2\right)\\ t_3 := x + t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+116}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -7.1 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -35000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-275}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-91}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 5
Error24.6
Cost1632
\[\begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := x + \left(z + t \cdot \left(b - a\right)\right)\\ t_3 := a + b \cdot \left(y + -2\right)\\ \mathbf{if}\;t \leq -132000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-159}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.62 \cdot 10^{-273}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-284}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-277}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-42}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 6
Error18.1
Cost1500
\[\begin{array}{l} t_1 := \left(x + z \cdot \left(1 - y\right)\right) + a\\ t_2 := x + \left(z + t \cdot \left(b - a\right)\right)\\ t_3 := a + b \cdot \left(y + -2\right)\\ \mathbf{if}\;t \leq -7000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-150}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-219}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-42}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) + -2\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 7
Error2.0
Cost1481
\[\begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;t \leq -9 \cdot 10^{-11} \lor \neg \left(t \leq 3 \cdot 10^{-42}\right):\\ \;\;\;\;t_1 + \left(\left(a - a \cdot t\right) - b \cdot \left(2 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(a + b \cdot \left(y + -2\right)\right)\\ \end{array} \]
Alternative 8
Error39.1
Cost1376
\[\begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;x \leq -1100000000000:\\ \;\;\;\;x + a\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-178}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-300}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-227}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-56}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
Alternative 9
Error39.6
Cost1376
\[\begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;x \leq -4000000000:\\ \;\;\;\;x + a\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-184}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-302}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-224}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.7 \cdot 10^{-59}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
Alternative 10
Error37.4
Cost1376
\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;x \leq -175000000:\\ \;\;\;\;x + a\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-302}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-137}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
Alternative 11
Error37.2
Cost1376
\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{+14}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-133}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.48 \cdot 10^{-300}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-136}:\\ \;\;\;\;a - a \cdot t\\ \mathbf{elif}\;x \leq 11800000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
Alternative 12
Error25.1
Cost1372
\[\begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) + -2\right)\\ t_2 := x + a \cdot \left(1 - t\right)\\ t_3 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+116}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-177}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 13
Error25.0
Cost1372
\[\begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) + -2\right)\\ t_2 := x + a \cdot \left(1 - t\right)\\ t_3 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+117}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-177}:\\ \;\;\;\;x + \left(z + t \cdot \left(b - a\right)\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-198}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 14
Error0.0
Cost1344
\[\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(y + t\right) + -2\right) \]
Alternative 15
Error15.1
Cost1236
\[\begin{array}{l} t_1 := \left(x + z \cdot \left(1 - y\right)\right) + a\\ t_2 := x + \left(z + t \cdot \left(b - a\right)\right)\\ t_3 := a + \left(x + b \cdot \left(y + -2\right)\right)\\ \mathbf{if}\;t \leq -8100000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.04 \cdot 10^{-151}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-17}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 16
Error2.2
Cost1225
\[\begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;t \leq -9.5 \lor \neg \left(t \leq 4\right):\\ \;\;\;\;t_1 + t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(a + b \cdot \left(y + -2\right)\right)\\ \end{array} \]
Alternative 17
Error36.8
Cost1112
\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;x \leq -1250000000:\\ \;\;\;\;x + a\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 75000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+82}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
Alternative 18
Error9.3
Cost1100
\[\begin{array}{l} t_1 := x + \left(z + t \cdot \left(b - a\right)\right)\\ \mathbf{if}\;t \leq -41000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-36}:\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) + a\\ \mathbf{elif}\;t \leq 1020:\\ \;\;\;\;\left(x + z\right) + \left(a + b \cdot \left(y + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 19
Error7.2
Cost1097
\[\begin{array}{l} \mathbf{if}\;t \leq -1.38 \cdot 10^{-36} \lor \neg \left(t \leq 1.1 \cdot 10^{-10}\right):\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) + t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + \left(a + b \cdot \left(y + -2\right)\right)\\ \end{array} \]
Alternative 20
Error44.4
Cost724
\[\begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+144}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{-132}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-184}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -2.95 \cdot 10^{-301}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+81}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 21
Error36.3
Cost652
\[\begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+159}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+39}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
Alternative 22
Error35.3
Cost652
\[\begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+161}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+39}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+115}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
Alternative 23
Error43.9
Cost460
\[\begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+144}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-131}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+81}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 24
Error35.6
Cost456
\[\begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+160}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+119}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
Alternative 25
Error43.6
Cost328
\[\begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+153}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
Alternative 26
Error53.5
Cost64
\[a \]

Error

Reproduce

herbie shell --seed 2022364 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))