Average Error: 0.0 → 0.0
Time: 20.4s
Precision: binary64
Cost: 13888
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
\[\mathsf{fma}\left(t + \left(y + -2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right) \]
(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 (+ t (+ y -2.0)) b (- x (fma (+ y -1.0) z (* a (+ t -1.0))))))
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((t + (y + -2.0)), b, (x - fma((y + -1.0), z, (a * (t + -1.0)))));
}
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(t + Float64(y + -2.0)), b, Float64(x - fma(Float64(y + -1.0), z, Float64(a * Float64(t + -1.0)))))
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[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision] * b + N[(x - N[(N[(y + -1.0), $MachinePrecision] * z + N[(a * N[(t + -1.0), $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
\mathsf{fma}\left(t + \left(y + -2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\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

    \[\leadsto \color{blue}{\mathsf{fma}\left(t + \left(y - 2\right), b, x - \mathsf{fma}\left(y - 1, z, \left(t + -1\right) \cdot a\right)\right)} \]
    Proof
    (fma.f64 (+.f64 t (-.f64 y 2)) b (-.f64 x (fma.f64 (-.f64 y 1) z (*.f64 (+.f64 t -1) a)))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 t y) 2)) b (-.f64 x (fma.f64 (-.f64 y 1) z (*.f64 (+.f64 t -1) a)))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 y t)) 2) b (-.f64 x (fma.f64 (-.f64 y 1) z (*.f64 (+.f64 t -1) a)))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (+.f64 y t) 2) b (-.f64 x (fma.f64 (-.f64 y 1) z (*.f64 (+.f64 t (Rewrite<= metadata-eval (neg.f64 1))) a)))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (+.f64 y t) 2) b (-.f64 x (fma.f64 (-.f64 y 1) z (*.f64 (Rewrite<= sub-neg_binary64 (-.f64 t 1)) a)))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (+.f64 y t) 2) b (-.f64 x (fma.f64 (-.f64 y 1) z (*.f64 (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 (-.f64 t 1)))) a)))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (+.f64 y t) 2) b (-.f64 x (fma.f64 (-.f64 y 1) z (Rewrite=> distribute-lft-neg-out_binary64 (neg.f64 (*.f64 (neg.f64 (-.f64 t 1)) a)))))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (+.f64 y t) 2) b (-.f64 x (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 (-.f64 y 1) z) (*.f64 (neg.f64 (-.f64 t 1)) a))))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (+.f64 y t) 2) b (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (neg.f64 (-.f64 t 1)) a)))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (+.f64 y t) 2) b (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)))): 0 points increase in error, 0 points decrease in error
    (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)))): 2 points increase in error, 0 points decrease in error
    (Rewrite<= +-commutative_binary64 (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b))): 0 points increase in error, 0 points decrease in error
  3. Final simplification0.0

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

Alternatives

Alternative 1
Error37.4
Cost2300
\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := b \cdot \left(t + -2\right)\\ t_3 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -1.1 \cdot 10^{+132}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -32500000000:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-28}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -1.44 \cdot 10^{-39}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-145}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-145}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-175}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-223}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-233}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7.4 \cdot 10^{-255}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-109}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 10^{+15}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{+166}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 2
Error20.0
Cost2024
\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := \left(x + t_1\right) - t \cdot a\\ t_3 := \left(x + y \cdot b\right) + a \cdot \left(1 - t\right)\\ t_4 := x + \left(z + b \cdot \left(t + -2\right)\right)\\ \mathbf{if}\;b \leq -1.6 \cdot 10^{+31}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -7.4 \cdot 10^{-39}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-152}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-237}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-291}:\\ \;\;\;\;\left(x + a\right) + t_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1950:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+118}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+177}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) + -2\right)\\ \end{array} \]
Alternative 3
Error19.0
Cost1760
\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := x + t_1\\ t_3 := \left(x + y \cdot b\right) + a \cdot \left(1 - t\right)\\ t_4 := x + \left(z + b \cdot \left(t + -2\right)\right)\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+31}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-28}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-236}:\\ \;\;\;\;t_2 + t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-293}:\\ \;\;\;\;\left(x + a\right) + t_1\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-114}:\\ \;\;\;\;t_2 - t \cdot a\\ \mathbf{elif}\;b \leq 360000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+120}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+175}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) + -2\right)\\ \end{array} \]
Alternative 4
Error38.8
Cost1644
\[\begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+132}:\\ \;\;\;\;b \cdot -2\\ \mathbf{elif}\;b \leq -530000000000:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-28}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-119}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-161}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-211}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{-254}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-109}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+14}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+118}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 6.1 \cdot 10^{+178}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot -2\\ \end{array} \]
Alternative 5
Error37.5
Cost1640
\[\begin{array}{l} t_1 := x + y \cdot b\\ t_2 := z \cdot \left(1 - y\right)\\ t_3 := b \cdot \left(t + -2\right)\\ \mathbf{if}\;b \leq -6.6 \cdot 10^{+153}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-210}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-254}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-214}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.5:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 6
Error21.4
Cost1628
\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := \left(x + y \cdot b\right) + a \cdot \left(1 - t\right)\\ t_3 := x + \left(z + b \cdot \left(t + -2\right)\right)\\ \mathbf{if}\;b \leq -7 \cdot 10^{+30}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -9.6 \cdot 10^{-37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-86}:\\ \;\;\;\;y \cdot b + t_1\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-232}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1050000:\\ \;\;\;\;\left(x + a\right) + t_1\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+119}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.56 \cdot 10^{+175}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) + -2\right)\\ \end{array} \]
Alternative 7
Error17.7
Cost1628
\[\begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := t_1 + \left(a - t \cdot a\right)\\ t_3 := x + \left(z + b \cdot \left(t + -2\right)\right)\\ \mathbf{if}\;y \leq -8.6 \cdot 10^{+97}:\\ \;\;\;\;t_1 + y \cdot b\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-146}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-188}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-243}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-146}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-8}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot b\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
Alternative 8
Error22.2
Cost1504
\[\begin{array}{l} t_1 := \left(x + a\right) - y \cdot z\\ t_2 := z + \left(x + a\right)\\ t_3 := x + \left(z + b \cdot \left(t + -2\right)\right)\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{+97}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-35}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-228}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 900:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+204}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot b\\ \end{array} \]
Alternative 9
Error37.9
Cost1380
\[\begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+138}:\\ \;\;\;\;b \cdot -2\\ \mathbf{elif}\;b \leq -320000000000:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-28}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-119}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-159}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-109}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+15}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+117}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 6.1 \cdot 10^{+178}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot -2\\ \end{array} \]
Alternative 10
Error39.0
Cost1380
\[\begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+133}:\\ \;\;\;\;b \cdot -2\\ \mathbf{elif}\;b \leq -65000000000:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-28}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-140}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-256}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-109}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+15}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+116}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 6.1 \cdot 10^{+178}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot -2\\ \end{array} \]
Alternative 11
Error37.5
Cost1376
\[\begin{array}{l} t_1 := b \cdot \left(t + -2\right)\\ \mathbf{if}\;b \leq -3.8 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -530000000000:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-28}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-141}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq -5.1 \cdot 10^{-254}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-109}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+14}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+166}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 12
Error28.0
Cost1372
\[\begin{array}{l} t_1 := z + \left(x + a\right)\\ t_2 := b \cdot \left(\left(t + y\right) + -2\right)\\ t_3 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -2.7 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -32000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-210}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{-254}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-111}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+167}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 13
Error28.0
Cost1372
\[\begin{array}{l} t_1 := z + \left(x + a\right)\\ t_2 := b \cdot \left(\left(t + y\right) + -2\right)\\ t_3 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -130000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-87}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-282}:\\ \;\;\;\;\left(x + a\right) - t \cdot a\\ \mathbf{elif}\;b \leq 1.62 \cdot 10^{-111}:\\ \;\;\;\;x + t_3\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 14
Error21.9
Cost1368
\[\begin{array}{l} t_1 := \left(x + a\right) + z \cdot \left(1 - y\right)\\ t_2 := x + \left(z + b \cdot \left(t + -2\right)\right)\\ \mathbf{if}\;y \leq -8.6 \cdot 10^{+97}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-229}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-147}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{elif}\;y \leq 900:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+204}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot b\\ \end{array} \]
Alternative 15
Error0.0
Cost1344
\[\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(t + y\right) + -2\right) \]
Alternative 16
Error36.6
Cost1248
\[\begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-35}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-129}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-175}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;a \leq 0.0025:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+86}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
Alternative 17
Error28.2
Cost1240
\[\begin{array}{l} t_1 := z + \left(x + a\right)\\ t_2 := b \cdot \left(\left(t + y\right) + -2\right)\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -32000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-242}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+167}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 18
Error8.0
Cost1224
\[\begin{array}{l} t_1 := \left(x + z \cdot \left(1 - y\right)\right) + \left(a - t \cdot a\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-14}:\\ \;\;\;\;\left(x + b \cdot \left(\left(t + y\right) + -2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 19
Error7.8
Cost1224
\[\begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := b \cdot \left(\left(t + y\right) + -2\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{+33}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-14}:\\ \;\;\;\;\left(x + t_2\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(a - t \cdot a\right)\\ \end{array} \]
Alternative 20
Error36.3
Cost1112
\[\begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;a \leq -1.16 \cdot 10^{+42}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-35}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-175}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;a \leq 0.0032:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
Alternative 21
Error45.6
Cost984
\[\begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-50}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-277}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-236}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+29}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+143}:\\ \;\;\;\;b \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 22
Error45.6
Cost856
\[\begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+42}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.7 \cdot 10^{-108}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+86}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+240}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
Alternative 23
Error44.5
Cost856
\[\begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-53}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-278}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-245}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-91}:\\ \;\;\;\;b \cdot -2\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+143}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 24
Error28.2
Cost848
\[\begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+17}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+151}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot b\\ \end{array} \]
Alternative 25
Error35.4
Cost456
\[\begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+169}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+146}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
Alternative 26
Error44.7
Cost328
\[\begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+43}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+240}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
Alternative 27
Error53.9
Cost64
\[a \]

Error

Reproduce

herbie shell --seed 2022325 
(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)))