?

Average Error: 0.0 → 0.0
Time: 34.4s
Precision: binary64
Cost: 20160

?

\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
↓
\[\mathsf{fma}\left(y - \left(2 - t\right), b, \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right) \]
(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
 (fma (- y (- 2.0 t)) b (fma a (- 1.0 t) (fma z (- 1.0 y) x))))
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 fma((y - (2.0 - t)), b, fma(a, (1.0 - t), fma(z, (1.0 - y), x)));
}

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 fma(Float64(y - Float64(2.0 - t)), b, fma(a, Float64(1.0 - t), fma(z, Float64(1.0 - y), x)))
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[(y - N[(2.0 - t), $MachinePrecision]), $MachinePrecision] * b + N[(a * N[(1.0 - t), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + x), $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
↓
\mathsf{fma}\left(y - \left(2 - t\right), b, \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\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

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

    [Start]0.0

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

    +-commutative [=>]0.0

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

    fma-def [=>]0.0

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

    sub-neg [=>]0.0

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

    associate-+l+ [=>]0.0

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

    metadata-eval [=>]0.0

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

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

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

    +-commutative [=>]0.0

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

    *-commutative [=>]0.0

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

    fma-def [=>]0.0

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

    neg-sub0 [=>]0.0

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

    associate--r- [=>]0.0

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

    neg-sub0 [<=]0.0

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

    +-commutative [=>]0.0

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

    sub-neg [<=]0.0

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

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

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

    +-commutative [=>]0.0

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

    *-commutative [=>]0.0

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

    fma-def [=>]0.0

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

    neg-sub0 [=>]0.0

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

    associate--r- [=>]0.0

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

    neg-sub0 [<=]0.0

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

    +-commutative [=>]0.0

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

    sub-neg [<=]0.0

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

  3. Final simplification0.0

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

Alternatives

Alternative 1
Error0.0
Cost7616
\[x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right) + b \cdot \left(\left(2 - t\right) - y\right)\right) \]
Alternative 2
Error34.8
Cost2428
\[\begin{array}{l} t_1 := x - t \cdot a\\ t_2 := a \cdot \left(1 - t\right)\\ t_3 := z + \left(a + x\right)\\ t_4 := b \cdot \left(-2 + \left(y + t\right)\right)\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+151}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2.12 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{+78}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{+20}:\\ \;\;\;\;a + y \cdot \left(b - z\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-34}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-75}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-307}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-194}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-104}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-88}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-20}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+25}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+107}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 3
Error41.1
Cost2305
\[\begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -6.4 \cdot 10^{+178}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-226}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-278}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;b \leq -7.6 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-264}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-120}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+30}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.3 \cdot 10^{+96}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+130}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+154} \lor \neg \left(b \leq 5.6 \cdot 10^{+189}\right) \land b \leq 1.7 \cdot 10^{+238}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot b\\ \end{array} \]
Alternative 4
Error38.9
Cost2169
\[\begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(t + -2\right)\\ \mathbf{if}\;b \leq -1.6 \cdot 10^{+122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-227}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{-278}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.45 \cdot 10^{-264}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-120}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+98} \lor \neg \left(b \leq 3.05 \cdot 10^{+147}\right) \land b \leq 1.15 \cdot 10^{+179}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 5
Error39.6
Cost2169
\[\begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(t + -2\right)\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-226}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5.1 \cdot 10^{-278}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-267}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{-122}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+30}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+95} \lor \neg \left(b \leq 1.7 \cdot 10^{+150}\right) \land b \leq 1.4 \cdot 10^{+178}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 6
Error28.1
Cost1900
\[\begin{array}{l} t_1 := z + \left(a + x\right)\\ t_2 := z \cdot \left(y + -1\right)\\ t_3 := b \cdot \left(-2 + \left(y + t\right)\right)\\ t_4 := x + \left(a - t \cdot a\right)\\ \mathbf{if}\;b \leq -4.9 \cdot 10^{+123}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{+67}:\\ \;\;\;\;a - t_2\\ \mathbf{elif}\;b \leq -1.48 \cdot 10^{-8}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-297}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-212}:\\ \;\;\;\;x - t_2\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-187}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-33}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+30}:\\ \;\;\;\;a + y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+87}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 7
Error28.8
Cost1504
\[\begin{array}{l} t_1 := z + \left(a + x\right)\\ t_2 := b \cdot \left(-2 + \left(y + t\right)\right)\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-165}:\\ \;\;\;\;a - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+30}:\\ \;\;\;\;a + y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+179}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 8
Error28.9
Cost1372
\[\begin{array}{l} t_1 := b \cdot \left(-2 + \left(y + t\right)\right)\\ t_2 := z \cdot \left(y + -1\right)\\ t_3 := a - t_2\\ t_4 := x - t_2\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+151}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{+61}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-258}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+25}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+124}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
Alternative 9
Error7.7
Cost1360
\[\begin{array}{l} t_1 := a + \left(z + \left(x - b \cdot \left(2 - y\right)\right)\right)\\ t_2 := x - z \cdot \left(y + -1\right)\\ t_3 := t_2 + t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -360000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-202}:\\ \;\;\;\;t_2 + y \cdot b\\ \mathbf{elif}\;t \leq 0.445:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 10
Error7.8
Cost1360
\[\begin{array}{l} t_1 := a + \left(z + \left(x - b \cdot \left(2 - y\right)\right)\right)\\ t_2 := x - z \cdot \left(y + -1\right)\\ t_3 := t_2 + t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -560000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-225}:\\ \;\;\;\;t_2 + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 0.53:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 11
Error0.0
Cost1344
\[\left(\left(x - z \cdot \left(y + -1\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(-2 + \left(y + t\right)\right) \]
Alternative 12
Error19.1
Cost1236
\[\begin{array}{l} t_1 := x + t \cdot \left(b - a\right)\\ t_2 := a + \left(z + \left(x + -2 \cdot b\right)\right)\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{-33}:\\ \;\;\;\;z + \left(x - b \cdot \left(2 - y\right)\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.96 \cdot 10^{-202}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;t \leq 6.2:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 13
Error15.1
Cost1232
\[\begin{array}{l} t_1 := a + \left(z + \left(x - b \cdot \left(2 - y\right)\right)\right)\\ t_2 := x + t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-202}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;t \leq 6.2:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 14
Error13.5
Cost1232
\[\begin{array}{l} t_1 := a + \left(z + \left(x - b \cdot \left(2 - y\right)\right)\right)\\ t_2 := \left(x - y \cdot z\right) + t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-202}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;t \leq 2.3:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 15
Error13.2
Cost1232
\[\begin{array}{l} t_1 := a + \left(z + \left(x - b \cdot \left(2 - y\right)\right)\right)\\ t_2 := \left(x - y \cdot z\right) + t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-202}:\\ \;\;\;\;\left(x - z \cdot \left(y + -1\right)\right) + y \cdot b\\ \mathbf{elif}\;t \leq 1.8:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 16
Error2.2
Cost1225
\[\begin{array}{l} \mathbf{if}\;t \leq -2900000 \lor \neg \left(t \leq 0.53\right):\\ \;\;\;\;\left(x - z \cdot \left(y + -1\right)\right) + t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(\left(x - b \cdot \left(2 - y\right)\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
Alternative 17
Error34.3
Cost1112
\[\begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+14}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-6}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-81}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-101}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq 4.5:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 18
Error19.2
Cost1104
\[\begin{array}{l} t_1 := a + \left(z + \left(x + -2 \cdot b\right)\right)\\ t_2 := x + t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+146}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-202}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;t \leq 3.4:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 19
Error46.3
Cost984
\[\begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+22}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-205}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-263}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.7 \cdot 10^{-194}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;a \leq 530000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+107}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
Alternative 20
Error35.1
Cost984
\[\begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+150}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{+23}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-258}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-213}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+130}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;a + x\\ \end{array} \]
Alternative 21
Error25.0
Cost976
\[\begin{array}{l} t_1 := z + \left(a + x\right)\\ t_2 := x + t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+146}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-202}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 1.6:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 22
Error28.3
Cost848
\[\begin{array}{l} t_1 := z + \left(a + x\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+157}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-202}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 6.2:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 23
Error45.6
Cost724
\[\begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+165}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-218}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-207}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+25}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
Alternative 24
Error45.7
Cost724
\[\begin{array}{l} \mathbf{if}\;a \leq -2.35 \cdot 10^{+17}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-205}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-263}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-192}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
Alternative 25
Error34.4
Cost720
\[\begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+20}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-258}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-213}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+137}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;a + x\\ \end{array} \]
Alternative 26
Error27.6
Cost585
\[\begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+154} \lor \neg \left(t \leq 6.2\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;z + \left(a + x\right)\\ \end{array} \]
Alternative 27
Error36.7
Cost456
\[\begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+207}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+30}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
Alternative 28
Error44.1
Cost328
\[\begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+24}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+101}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
Alternative 29
Error53.7
Cost64
\[a \]

Error

Reproduce?

herbie shell --seed 2023031 
(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)))