Average Error: 14.6 → 4.0
Time: 32.6s
Precision: binary64
Cost: 8904
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
\[\begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ t_2 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_2 \leq -4 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t - \frac{x}{\frac{z}{a - y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
(FPCore (x y z t a) :precision binary64 (+ x (* (- y z) (/ (- t x) (- a z)))))
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t x) (/ (- y z) (- a z)) x))
        (t_2 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (<= t_2 -4e-279) t_1 (if (<= t_2 0.0) (- t (/ x (/ z (- a y)))) t_1))))
double code(double x, double y, double z, double t, double a) {
	return x + ((y - z) * ((t - x) / (a - z)));
}
double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t - x), ((y - z) / (a - z)), x);
	double t_2 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if (t_2 <= -4e-279) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t - (x / (z / (a - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}
function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
end
function code(x, y, z, t, a)
	t_1 = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -4e-279)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t - Float64(x / Float64(z / Float64(a - y))));
	else
		tmp = t_1;
	end
	return tmp
end
code[x_, y_, z_, t_, a_] := N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-279], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t - N[(x / N[(z / N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
\begin{array}{l}
t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\
t_2 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\
\mathbf{if}\;t_2 \leq -4 \cdot 10^{-279}:\\
\;\;\;\;t_1\\

\mathbf{elif}\;t_2 \leq 0:\\
\;\;\;\;t - \frac{x}{\frac{z}{a - y}}\\

\mathbf{else}:\\
\;\;\;\;t_1\\


\end{array}

Error

Derivation

  1. Split input into 2 regimes
  2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.00000000000000022e-279 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

    1. Initial program 7.2

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
    2. Simplified4.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
      Proof
      (fma.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z)) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z))) x)): 2 points increase in error, 3 points decrease in error
      (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (-.f64 t x) (-.f64 y z)) (-.f64 a z))) x): 86 points increase in error, 9 points decrease in error
      (+.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 y z) (-.f64 t x))) (-.f64 a z)) x): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) x): 35 points increase in error, 86 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))): 0 points increase in error, 0 points decrease in error

    if -4.00000000000000022e-279 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

    1. Initial program 60.3

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
    2. Simplified58.7

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
      Proof
      (fma.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z)) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z))) x)): 2 points increase in error, 3 points decrease in error
      (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (-.f64 t x) (-.f64 y z)) (-.f64 a z))) x): 86 points increase in error, 9 points decrease in error
      (+.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 y z) (-.f64 t x))) (-.f64 a z)) x): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) x): 35 points increase in error, 86 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))): 0 points increase in error, 0 points decrease in error
    3. Taylor expanded in z around inf 12.6

      \[\leadsto \color{blue}{\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t} \]
    4. Simplified3.0

      \[\leadsto \color{blue}{t + \frac{a - y}{z} \cdot \left(t - x\right)} \]
      Proof
      (+.f64 t (*.f64 (/.f64 (-.f64 a y) z) (-.f64 t x))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (*.f64 (/.f64 (Rewrite<= unsub-neg_binary64 (+.f64 a (neg.f64 y))) z) (-.f64 t x))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (*.f64 (/.f64 (+.f64 a (Rewrite<= mul-1-neg_binary64 (*.f64 -1 y))) z) (-.f64 t x))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (*.f64 (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 y) a)) z) (-.f64 t x))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (*.f64 (/.f64 (+.f64 (*.f64 -1 y) (Rewrite<= *-lft-identity_binary64 (*.f64 1 a))) z) (-.f64 t x))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (*.f64 (/.f64 (+.f64 (*.f64 -1 y) (*.f64 (Rewrite<= metadata-eval (neg.f64 -1)) a)) z) (-.f64 t x))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (*.f64 (/.f64 (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (*.f64 -1 y) (*.f64 -1 a))) z) (-.f64 t x))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (Rewrite<= associate-/r/_binary64 (/.f64 (-.f64 (*.f64 -1 y) (*.f64 -1 a)) (/.f64 z (-.f64 t x))))): 26 points increase in error, 29 points decrease in error
      (+.f64 t (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 (*.f64 -1 y) (*.f64 -1 a)) (-.f64 t x)) z))): 48 points increase in error, 25 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (*.f64 (-.f64 (*.f64 -1 y) (*.f64 -1 a)) (-.f64 t x)) z) t)): 0 points increase in error, 0 points decrease in error
    5. Taylor expanded in t around 0 12.7

      \[\leadsto t + \color{blue}{-1 \cdot \frac{x \cdot \left(a - y\right)}{z}} \]
    6. Simplified3.3

      \[\leadsto t + \color{blue}{\left(-\frac{x}{\frac{z}{a - y}}\right)} \]
      Proof
      (neg.f64 (/.f64 x (/.f64 z (-.f64 a y)))): 0 points increase in error, 0 points decrease in error
      (neg.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 x (-.f64 a y)) z))): 56 points increase in error, 36 points decrease in error
      (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (*.f64 x (-.f64 a y)) z))): 0 points increase in error, 0 points decrease in error
  3. Recombined 2 regimes into one program.
  4. Final simplification4.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -4 \cdot 10^{-279}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0:\\ \;\;\;\;t - \frac{x}{\frac{z}{a - y}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \]

Alternatives

Alternative 1
Error6.7
Cost2888
\[\begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{-259}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \left(z - y\right)\\ \end{array} \]
Alternative 2
Error6.7
Cost2632
\[\begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-252}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 3
Error28.2
Cost1896
\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{+196}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{+110}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1120000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.04 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-171}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 15600000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
Alternative 4
Error28.2
Cost1896
\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{+195}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{+114}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -420000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-61}:\\ \;\;\;\;t - \frac{a}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq -7.3 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 7000000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
Alternative 5
Error27.1
Cost1632
\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{+197}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{+111}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 14000000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
Alternative 6
Error29.1
Cost1372
\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_3 := \frac{t}{\frac{z - a}{z}}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+94}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{+68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-205}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 7
Error29.1
Cost1372
\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ t_2 := \frac{t}{\frac{z - a}{z}}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+68}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-208}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 8
Error29.1
Cost1372
\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ t_2 := \frac{t}{\frac{z - a}{z}}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.55 \cdot 10^{+68}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-198}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+112}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 9
Error30.8
Cost1240
\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -8 \cdot 10^{+196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.9 \cdot 10^{+44}:\\ \;\;\;\;z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-40}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 10
Error30.9
Cost1240
\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -2.45 \cdot 10^{+193}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9 \cdot 10^{+43}:\\ \;\;\;\;z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-40}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
Alternative 11
Error30.9
Cost1240
\[\begin{array}{l} t_1 := x - \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -9 \cdot 10^{+192}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{+43}:\\ \;\;\;\;z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-41}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
Alternative 12
Error30.8
Cost1240
\[\begin{array}{l} t_1 := x - \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -1.95 \cdot 10^{+197}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{+44}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-41}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
Alternative 13
Error28.7
Cost1236
\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+196}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{+111}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.15 \cdot 10^{-139}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;a \leq 17200000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
Alternative 14
Error21.4
Cost1104
\[\begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+148}:\\ \;\;\;\;t - \frac{a}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+18}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-22}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+42}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
Alternative 15
Error19.4
Cost1104
\[\begin{array}{l} t_1 := t - \frac{x}{\frac{z}{a - y}}\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -150000000:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-21}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+48}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 16
Error23.5
Cost972
\[\begin{array}{l} t_1 := t - \frac{a}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.36 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+50}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 17
Error17.5
Cost968
\[\begin{array}{l} t_1 := t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -5400000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+42}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 18
Error17.0
Cost968
\[\begin{array}{l} t_1 := t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -242000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+48}:\\ \;\;\;\;x - \frac{z - y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 19
Error17.0
Cost968
\[\begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -46000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+44}:\\ \;\;\;\;x - \frac{z - y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 20
Error20.4
Cost840
\[\begin{array}{l} t_1 := t + y \cdot \frac{x - t}{z}\\ \mathbf{if}\;z \leq -5800000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+52}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 21
Error35.8
Cost716
\[\begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
Alternative 22
Error35.8
Cost716
\[\begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+97}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+111}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
Alternative 23
Error32.7
Cost712
\[\begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1020000000000:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 24
Error31.7
Cost712
\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 820000000000:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 25
Error35.6
Cost328
\[\begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+95}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
Alternative 26
Error62.1
Cost64
\[0 \]
Alternative 27
Error45.6
Cost64
\[t \]

Error

Reproduce

herbie shell --seed 2022330 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))