Average Error: 0.0 → 0.0
Time: 49.8s
Precision: binary64
Cost: 20160
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
↓
\[\mathsf{fma}\left(y + \left(t - 2\right), b, \mathsf{fma}\left(z, 1 - y, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right) \]
(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 (- t 2.0)) b (fma z (- 1.0 y) (fma a (- 1.0 t) 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 + (t - 2.0)), b, fma(z, (1.0 - y), fma(a, (1.0 - t), 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(t - 2.0)), b, fma(z, Float64(1.0 - y), fma(a, Float64(1.0 - t), 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[(t - 2.0), $MachinePrecision]), $MachinePrecision] * b + N[(z * N[(1.0 - y), $MachinePrecision] + N[(a * N[(1.0 - t), $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(t - 2\right), b, \mathsf{fma}\left(z, 1 - y, \mathsf{fma}\left(a, 1 - t, 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

    \[\leadsto \color{blue}{\mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)} \]
    Proof
    (fma.f64 (+.f64 y (+.f64 t -2)) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (+.f64 y (+.f64 t (Rewrite<= metadata-eval (neg.f64 2)))) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 y t) (neg.f64 2))) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (Rewrite<= sub-neg_binary64 (-.f64 (+.f64 y t) 2)) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (Rewrite<= unsub-neg_binary64 (+.f64 1 (neg.f64 y))) (fma.f64 a (-.f64 1 t) x))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (Rewrite<= +-commutative_binary64 (+.f64 (neg.f64 y) 1)) (fma.f64 a (-.f64 1 t) x))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 y)) 1) (fma.f64 a (-.f64 1 t) x))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (Rewrite<= associate--r-_binary64 (-.f64 0 (-.f64 y 1))) (fma.f64 a (-.f64 1 t) x))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 y 1))) (fma.f64 a (-.f64 1 t) x))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (neg.f64 (-.f64 y 1)) (fma.f64 a (Rewrite<= unsub-neg_binary64 (+.f64 1 (neg.f64 t))) x))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (neg.f64 (-.f64 y 1)) (fma.f64 a (Rewrite<= +-commutative_binary64 (+.f64 (neg.f64 t) 1)) x))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (neg.f64 (-.f64 y 1)) (fma.f64 a (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 t)) 1) x))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (neg.f64 (-.f64 y 1)) (fma.f64 a (Rewrite<= associate--r-_binary64 (-.f64 0 (-.f64 t 1))) x))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (neg.f64 (-.f64 y 1)) (fma.f64 a (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 t 1))) x))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (neg.f64 (-.f64 y 1)) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 a (neg.f64 (-.f64 t 1))) x)))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (neg.f64 (-.f64 y 1)) (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (neg.f64 (-.f64 t 1)) a)) x))): 0 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (neg.f64 (-.f64 y 1)) (Rewrite<= +-commutative_binary64 (+.f64 x (*.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<= fma-def_binary64 (+.f64 (*.f64 z (neg.f64 (-.f64 y 1))) (+.f64 x (*.f64 (neg.f64 (-.f64 t 1)) a))))): 2 points increase in error, 0 points decrease in error
    (fma.f64 (-.f64 (+.f64 y t) 2) b (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (neg.f64 (-.f64 y 1)) z)) (+.f64 x (*.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 (*.f64 (neg.f64 (-.f64 y 1)) z) x) (*.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 (Rewrite<= +-commutative_binary64 (+.f64 x (*.f64 (neg.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 (+.f64 (Rewrite<= cancel-sign-sub-inv_binary64 (-.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)))): 0 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

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

Alternatives

Alternative 1
Error30.4
Cost2692
\[\begin{array}{l} t_1 := x + \left(z + a\right)\\ t_2 := x + a \cdot \left(1 - t\right)\\ t_3 := z + b \cdot \left(t - 2\right)\\ t_4 := y \cdot \left(b - z\right)\\ t_5 := b \cdot \left(-2 + \left(y + t\right)\right)\\ t_6 := x + t_5\\ t_7 := a + t_5\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+113}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+28}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -3.730607802328015 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.4839014187145083 \cdot 10^{-145}:\\ \;\;\;\;z - b \cdot 2\\ \mathbf{elif}\;y \leq -8.930741323974776 \cdot 10^{-189}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq -3.356775202303174 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.4712600847828604 \cdot 10^{-275}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq -7.35106379611236 \cdot 10^{-283}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.615699183790719 \cdot 10^{-305}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y \leq 3.9136452976539704 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.5060454037526894 \cdot 10^{-205}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.0478789540777642 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.8723620902757192 \cdot 10^{-153}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y \leq 1.2609296086578406 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.052758852143905 \cdot 10^{-36}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+92}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]
Alternative 2
Error29.3
Cost2552
\[\begin{array}{l} t_1 := z + b \cdot \left(t - 2\right)\\ t_2 := x + a \cdot \left(1 - t\right)\\ t_3 := a + b \cdot \left(-2 + \left(y + t\right)\right)\\ t_4 := \left(y + \left(t - 2\right)\right) \cdot b - y \cdot z\\ t_5 := x + \left(z + a\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+113}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+28}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -5.353268731909357 \cdot 10^{-118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.869801489297713 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.35106379611236 \cdot 10^{-283}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -7.615699183790719 \cdot 10^{-305}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.9136452976539704 \cdot 10^{-285}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 1.5060454037526894 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.0478789540777642 \cdot 10^{-176}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 1.8723620902757192 \cdot 10^{-153}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.2609296086578406 \cdot 10^{-101}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 9.052758852143905 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+92}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]
Alternative 3
Error29.9
Cost2032
\[\begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := x + \left(z + a\right)\\ t_3 := a + b \cdot \left(-2 + \left(y + t\right)\right)\\ t_4 := y \cdot \left(b - z\right)\\ t_5 := z + b \cdot \left(t - 2\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+113}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -5.353268731909357 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.869801489297713 \cdot 10^{-183}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -7.35106379611236 \cdot 10^{-283}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7.615699183790719 \cdot 10^{-305}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.9136452976539704 \cdot 10^{-285}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.5060454037526894 \cdot 10^{-205}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 2.0478789540777642 \cdot 10^{-176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.8723620902757192 \cdot 10^{-153}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.2609296086578406 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.052758852143905 \cdot 10^{-36}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]
Alternative 4
Error25.4
Cost2024
\[\begin{array}{l} t_1 := \left(y + \left(t - 2\right)\right) \cdot b - y \cdot z\\ t_2 := y \cdot b + \left(x + a \cdot \left(1 - t\right)\right)\\ t_3 := x + \left(z + a\right)\\ t_4 := b \cdot \left(-2 + \left(y + t\right)\right)\\ t_5 := x + t_4\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+159}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -6.37129763460183 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.1670893755167368 \cdot 10^{-258}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 4.610917539953622 \cdot 10^{-307}:\\ \;\;\;\;a + t_4\\ \mathbf{elif}\;z \leq 5.569434505190601 \cdot 10^{-211}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.076330123999511 \cdot 10^{-113}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 1.6961289837747637 \cdot 10^{-43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.112381576878481 \cdot 10^{+45}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+108}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \]
Alternative 5
Error24.0
Cost1892
\[\begin{array}{l} t_1 := \left(y + \left(t - 2\right)\right) \cdot b - y \cdot z\\ t_2 := y \cdot b + \left(x + a \cdot \left(1 - t\right)\right)\\ t_3 := x + \left(z + a\right)\\ t_4 := x + b \cdot \left(-2 + \left(y + t\right)\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+159}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -6.37129763460183 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.610917539953622 \cdot 10^{-307}:\\ \;\;\;\;a + \left(x + b \cdot \left(y - 2\right)\right)\\ \mathbf{elif}\;z \leq 5.569434505190601 \cdot 10^{-211}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.076330123999511 \cdot 10^{-113}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.6961289837747637 \cdot 10^{-43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.112381576878481 \cdot 10^{+45}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+108}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \]
Alternative 6
Error32.3
Cost1772
\[\begin{array}{l} t_1 := x - t \cdot a\\ t_2 := x + \left(z + a\right)\\ t_3 := y \cdot \left(b - z\right)\\ \mathbf{if}\;t \leq -1.12 \cdot 10^{+229}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -16733060379087469000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.0239468909326105 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq -1.667705203329412 \cdot 10^{-116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8.582588039470876 \cdot 10^{-135}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.296153814822923 \cdot 10^{-253}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.944647353184704 \cdot 10^{-290}:\\ \;\;\;\;z - b \cdot 2\\ \mathbf{elif}\;t \leq 942635700843.2919:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{+59}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+182}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 7
Error29.4
Cost1768
\[\begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := x + \left(z + a\right)\\ t_3 := y \cdot \left(b - z\right)\\ t_4 := z + b \cdot \left(t - 2\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+113}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -5.353268731909357 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.869801489297713 \cdot 10^{-183}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -7.318161527358649 \cdot 10^{-273}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.1320366555343017 \cdot 10^{-298}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 3.9136452976539704 \cdot 10^{-285}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.5060454037526894 \cdot 10^{-205}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 1.2609296086578406 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.052758852143905 \cdot 10^{-36}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 8
Error12.4
Cost1752
\[\begin{array}{l} t_1 := b \cdot \left(-2 + \left(y + t\right)\right)\\ t_2 := t_1 + \left(a + z \cdot \left(1 - y\right)\right)\\ t_3 := y \cdot b + \left(x + a \cdot \left(1 - t\right)\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 111224.30086519121:\\ \;\;\;\;t_1 + \left(a + \left(z + x\right)\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+147}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 9
Error31.1
Cost1640
\[\begin{array}{l} t_1 := x + \left(z + a\right)\\ t_2 := t \cdot \left(b - a\right)\\ t_3 := b \cdot \left(y - 2\right)\\ t_4 := a + t_3\\ \mathbf{if}\;t \leq -7 \cdot 10^{+164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -16733060379087469000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.0239468909326105 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq -1.667705203329412 \cdot 10^{-116}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -8.582588039470876 \cdot 10^{-135}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -7.437226096839237 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.944647353184704 \cdot 10^{-290}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 2.658998345829016 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.2204105472883876 \cdot 10^{-19}:\\ \;\;\;\;x + t_3\\ \mathbf{elif}\;t \leq 942635700843.2919:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 10
Error29.8
Cost1376
\[\begin{array}{l} t_1 := x + \left(z + a\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7 \cdot 10^{+164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -16733060379087469000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.0239468909326105 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq -1.667705203329412 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.582588039470876 \cdot 10^{-135}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -1.296153814822923 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.944647353184704 \cdot 10^{-290}:\\ \;\;\;\;z - b \cdot 2\\ \mathbf{elif}\;t \leq 942635700843.2919:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 11
Error30.3
Cost1376
\[\begin{array}{l} t_1 := x + \left(z + a\right)\\ t_2 := t \cdot \left(b - a\right)\\ t_3 := a + b \cdot \left(y - 2\right)\\ \mathbf{if}\;t \leq -7 \cdot 10^{+164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -16733060379087469000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.0239468909326105 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq -1.667705203329412 \cdot 10^{-116}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -8.582588039470876 \cdot 10^{-135}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -7.437226096839237 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.944647353184704 \cdot 10^{-290}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 942635700843.2919:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 12
Error15.2
Cost1360
\[\begin{array}{l} t_1 := b \cdot \left(-2 + \left(y + t\right)\right)\\ t_2 := t_1 + \left(a + \left(z + x\right)\right)\\ \mathbf{if}\;t \leq -1.12 \cdot 10^{+229}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -16733060379087469000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.0239468909326105 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 - t \cdot a\\ \end{array} \]
Alternative 13
Error15.2
Cost1360
\[\begin{array}{l} t_1 := b \cdot \left(-2 + \left(y + t\right)\right)\\ t_2 := t_1 + \left(a + \left(z + x\right)\right)\\ \mathbf{if}\;t \leq -1.12 \cdot 10^{+229}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -16733060379087469000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.0239468909326105 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(a - t \cdot a\right)\\ \end{array} \]
Alternative 14
Error11.2
Cost1356
\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := b \cdot \left(-2 + \left(y + t\right)\right)\\ t_3 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -3.424960343343039 \cdot 10^{+36}:\\ \;\;\;\;t_2 + \left(a + t_1\right)\\ \mathbf{elif}\;a \leq -45485211.15641851:\\ \;\;\;\;y \cdot b + \left(x + t_3\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+123}:\\ \;\;\;\;\left(x + t_1\right) + t_2\\ \mathbf{else}:\\ \;\;\;\;t_2 + t_3\\ \end{array} \]
Alternative 15
Error9.0
Cost1356
\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := b \cdot \left(-2 + \left(y + t\right)\right)\\ t_3 := t_2 + \left(x + a \cdot \left(1 - t\right)\right)\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{+171}:\\ \;\;\;\;t_2 + \left(a + t_1\right)\\ \mathbf{elif}\;a \leq -0.9682999720078009:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+123}:\\ \;\;\;\;\left(x + t_1\right) + t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 16
Error5.1
Cost1352
\[\begin{array}{l} t_1 := b \cdot \left(-2 + \left(y + t\right)\right) + \left(a + \left(z + x\right)\right)\\ \mathbf{if}\;b \leq -3.41310942603858 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.1084241365096605 \cdot 10^{-35}:\\ \;\;\;\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 17
Error3.3
Cost1352
\[\begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := b \cdot \left(-2 + \left(y + t\right)\right) + \left(a + t_1\right)\\ \mathbf{if}\;b \leq -1.3970115083720693 \cdot 10^{-72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.1084241365096605 \cdot 10^{-35}:\\ \;\;\;\;\left(t_1 + a \cdot \left(1 - t\right)\right) + y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 18
Error0.0
Cost1344
\[b \cdot \left(-2 + \left(y + t\right)\right) + \left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) \]
Alternative 19
Error0.0
Cost1344
\[\left(\left(x + z \cdot \left(1 - y\right)\right) + \left(a - t \cdot a\right)\right) + b \cdot \left(-2 + \left(y + t\right)\right) \]
Alternative 20
Error31.3
Cost1112
\[\begin{array}{l} t_1 := x + \left(z + a\right)\\ \mathbf{if}\;t \leq -1.12 \cdot 10^{+229}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -16733060379087469000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.0239468909326105 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq -1.296153814822923 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.944647353184704 \cdot 10^{-290}:\\ \;\;\;\;z - b \cdot 2\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot a\\ \end{array} \]
Alternative 21
Error30.5
Cost848
\[\begin{array}{l} t_1 := x + \left(z + a\right)\\ \mathbf{if}\;t \leq -1.12 \cdot 10^{+229}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -16733060379087469000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.0239468909326105 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot a\\ \end{array} \]
Alternative 22
Error37.1
Cost720
\[\begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+201}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.6362699700259369 \cdot 10^{-286}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;z \leq 1.3491969247671918 \cdot 10^{-263}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+88}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
Alternative 23
Error36.6
Cost720
\[\begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+201}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.3331088114996612 \cdot 10^{-297}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;z \leq 1.3491969247671918 \cdot 10^{-263}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+88}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
Alternative 24
Error37.2
Cost720
\[\begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+201}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.6362699700259369 \cdot 10^{-286}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;z \leq 5.569434505190601 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+88}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
Alternative 25
Error36.7
Cost456
\[\begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+201}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+88}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
Alternative 26
Error43.9
Cost328
\[\begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+150}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4.2062554921828315 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
Alternative 27
Error53.4
Cost64
\[z \]

Error

Reproduce

herbie shell --seed 2022316 
(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)))