Average Error: 14.8 → 4.2
Time: 28.9s
Precision: binary64
Cost: 11604
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
\[\begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-262}:\\ \;\;\;\;t + \frac{a - y}{\frac{-z}{x}}\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-144}:\\ \;\;\;\;t\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+199}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
(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 (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -1e-296)
     t_1
     (if (<= t_2 5e-262)
       (+ t (/ (- a y) (/ (- z) x)))
       (if (<= t_2 4e-147)
         t_1
         (if (<= t_2 5e-144) t (if (<= t_2 2e+199) t_2 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 + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -1e-296) {
		tmp = t_1;
	} else if (t_2 <= 5e-262) {
		tmp = t + ((a - y) / (-z / x));
	} else if (t_2 <= 4e-147) {
		tmp = t_1;
	} else if (t_2 <= 5e-144) {
		tmp = t;
	} else if (t_2 <= 2e+199) {
		tmp = t_2;
	} 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(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -1e-296)
		tmp = t_1;
	elseif (t_2 <= 5e-262)
		tmp = Float64(t + Float64(Float64(a - y) / Float64(Float64(-z) / x)));
	elseif (t_2 <= 4e-147)
		tmp = t_1;
	elseif (t_2 <= 5e-144)
		tmp = t;
	elseif (t_2 <= 2e+199)
		tmp = t_2;
	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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-296], t$95$1, If[LessEqual[t$95$2, 5e-262], N[(t + N[(N[(a - y), $MachinePrecision] / N[((-z) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e-147], t$95$1, If[LessEqual[t$95$2, 5e-144], t, If[LessEqual[t$95$2, 2e+199], t$95$2, 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(y - z\right) \cdot \frac{t - x}{a - z}\\
\mathbf{if}\;t_2 \leq -1 \cdot 10^{-296}:\\
\;\;\;\;t_1\\

\mathbf{elif}\;t_2 \leq 5 \cdot 10^{-262}:\\
\;\;\;\;t + \frac{a - y}{\frac{-z}{x}}\\

\mathbf{elif}\;t_2 \leq 4 \cdot 10^{-147}:\\
\;\;\;\;t_1\\

\mathbf{elif}\;t_2 \leq 5 \cdot 10^{-144}:\\
\;\;\;\;t\\

\mathbf{elif}\;t_2 \leq 2 \cdot 10^{+199}:\\
\;\;\;\;t_2\\

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


\end{array}

Error

Derivation

  1. Split input into 4 regimes
  2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1e-296 or 4.99999999999999992e-262 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 3.9999999999999999e-147 or 2.00000000000000019e199 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

    1. Initial program 8.6

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
    2. Simplified4.4

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
      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)): 5 points increase in error, 1 points decrease in error
      (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (-.f64 t x) (-.f64 y z)) (-.f64 a z))) x): 101 points increase in error, 17 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): 37 points increase in error, 96 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 -1e-296 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.99999999999999992e-262

    1. Initial program 59.7

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
    2. Simplified56.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
      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)): 5 points increase in error, 1 points decrease in error
      (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (-.f64 t x) (-.f64 y z)) (-.f64 a z))) x): 101 points increase in error, 17 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): 37 points increase in error, 96 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 13.5

      \[\leadsto \color{blue}{\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t} \]
    4. Simplified3.7

      \[\leadsto \color{blue}{t + \frac{a - y}{z} \cdot \left(t - x\right)} \]
      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))))): 21 points increase in error, 38 points decrease in error
      (+.f64 t (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 (*.f64 -1 y) (*.f64 -1 a)) (-.f64 t x)) z))): 49 points increase in error, 22 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. Applied egg-rr3.3

      \[\leadsto t + \color{blue}{\frac{a - y}{\frac{z}{t - x}}} \]
    6. Taylor expanded in t around 0 3.2

      \[\leadsto t + \frac{a - y}{\color{blue}{-1 \cdot \frac{z}{x}}} \]
    7. Simplified3.2

      \[\leadsto t + \frac{a - y}{\color{blue}{\frac{-z}{x}}} \]
      Proof
      (/.f64 (neg.f64 z) x): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 z)) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*r/_binary64 (*.f64 -1 (/.f64 z x))): 0 points increase in error, 0 points decrease in error

    if 3.9999999999999999e-147 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.9999999999999998e-144

    1. Initial program 12.7

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
    2. Applied egg-rr12.5

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]
    3. Taylor expanded in z around inf 44.0

      \[\leadsto \color{blue}{t} \]

    if 4.9999999999999998e-144 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2.00000000000000019e199

    1. Initial program 4.1

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
  3. Recombined 4 regimes into one program.
  4. Final simplification4.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-296}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 5 \cdot 10^{-262}:\\ \;\;\;\;t + \frac{a - y}{\frac{-z}{x}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 4 \cdot 10^{-147}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 5 \cdot 10^{-144}:\\ \;\;\;\;t\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{+199}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \]

Alternatives

Alternative 1
Error27.4
Cost1632
\[\begin{array}{l} t_1 := x - t \cdot \frac{z}{a - z}\\ t_2 := t - a \cdot \frac{x}{z}\\ t_3 := \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;z \leq -4.3675116054081444 \cdot 10^{+223}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.1335821810477645 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -2.0425848820788784 \cdot 10^{+138}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.6929151398611285 \cdot 10^{+121}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-129}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.7284250513439414 \cdot 10^{+182}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 2
Error26.6
Cost1500
\[\begin{array}{l} t_1 := x - t \cdot \frac{z}{a - z}\\ t_2 := t - a \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -4.3675116054081444 \cdot 10^{+223}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.1335821810477645 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -2.0425848820788784 \cdot 10^{+138}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.6929151398611285 \cdot 10^{+121}:\\ \;\;\;\;\frac{-y}{\frac{a - z}{x}}\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-105}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.7284250513439414 \cdot 10^{+182}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 3
Error18.8
Cost1496
\[\begin{array}{l} t_1 := x - t \cdot \frac{z}{a - z}\\ t_2 := t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{if}\;z \leq -4.6838539095067016 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-111}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 398702618180.705:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 4
Error9.7
Cost1352
\[\begin{array}{l} \mathbf{if}\;z \leq -2.1829530167142483 \cdot 10^{+132}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 7.427021552834866 \cdot 10^{+176}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(\frac{a}{z} + 1\right) \cdot \left(\left(t - x\right) \cdot \frac{a - y}{z}\right)\\ \end{array} \]
Alternative 5
Error30.0
Cost1240
\[\begin{array}{l} t_1 := t - a \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -4.3675116054081444 \cdot 10^{+223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.1335821810477645 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -2.0425848820788784 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6929151398611285 \cdot 10^{+121}:\\ \;\;\;\;\frac{-y}{\frac{a - z}{x}}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-66}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 2.4552359756635686 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 6
Error22.4
Cost1236
\[\begin{array}{l} t_1 := x - t \cdot \frac{z}{a - z}\\ t_2 := t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -1.3624031642850368 \cdot 10^{+123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-129}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-60}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 1.0690402058738972 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 7
Error14.5
Cost1232
\[\begin{array}{l} t_1 := x + t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -8.095858740676062 \cdot 10^{+171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.2464893016163453 \cdot 10^{+78}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq -1.615965449925039 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.5697656859265602 \cdot 10^{+28}:\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a - y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 8
Error36.0
Cost1108
\[\begin{array}{l} t_1 := x - t \cdot \frac{z}{a}\\ \mathbf{if}\;z \leq -4.3675116054081444 \cdot 10^{+223}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.3624031642850368 \cdot 10^{+123}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-243}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.0690402058738972 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
Alternative 9
Error36.0
Cost1108
\[\begin{array}{l} t_1 := t \cdot \left(\frac{a}{z} + 1\right)\\ t_2 := x - t \cdot \frac{z}{a}\\ \mathbf{if}\;z \leq -4.3675116054081444 \cdot 10^{+223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.3624031642850368 \cdot 10^{+123}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-253}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-243}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.0690402058738972 \cdot 10^{+136}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 10
Error18.5
Cost1104
\[\begin{array}{l} t_1 := x - t \cdot \frac{z}{a - z}\\ t_2 := t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -1.3624031642850368 \cdot 10^{+123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-83}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.0690402058738972 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 11
Error18.5
Cost1104
\[\begin{array}{l} t_1 := x - t \cdot \frac{z}{a - z}\\ \mathbf{if}\;z \leq -1.3624031642850368 \cdot 10^{+123}:\\ \;\;\;\;t + \frac{a - y}{\frac{-z}{x}}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-83}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.0690402058738972 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \end{array} \]
Alternative 12
Error9.7
Cost1096
\[\begin{array}{l} \mathbf{if}\;z \leq -2.1829530167142483 \cdot 10^{+132}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 7.427021552834866 \cdot 10^{+176}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a - y}}\\ \end{array} \]
Alternative 13
Error38.1
Cost976
\[\begin{array}{l} \mathbf{if}\;z \leq -4.3675116054081444 \cdot 10^{+223}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.3624031642850368 \cdot 10^{+123}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-253}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-243}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.815666572005882 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
Alternative 14
Error32.5
Cost976
\[\begin{array}{l} t_1 := t \cdot \left(\frac{a}{z} + 1\right)\\ \mathbf{if}\;z \leq -4.3675116054081444 \cdot 10^{+223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.3624031642850368 \cdot 10^{+123}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-66}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 1.815666572005882 \cdot 10^{+125}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 15
Error32.2
Cost976
\[\begin{array}{l} t_1 := t \cdot \left(\frac{a}{z} + 1\right)\\ \mathbf{if}\;z \leq -4.3675116054081444 \cdot 10^{+223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.3624031642850368 \cdot 10^{+123}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-66}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 1.815666572005882 \cdot 10^{+125}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 16
Error16.9
Cost968
\[\begin{array}{l} t_1 := t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{if}\;z \leq -4.6838539095067016 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 398702618180.705:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 17
Error16.7
Cost968
\[\begin{array}{l} \mathbf{if}\;z \leq -4.6838539095067016 \cdot 10^{+38}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 398702618180.705:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a - y}}\\ \end{array} \]
Alternative 18
Error35.9
Cost592
\[\begin{array}{l} \mathbf{if}\;z \leq -2.0425848820788784 \cdot 10^{+138}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.3624031642850368 \cdot 10^{+123}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq -7.608294193770039 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.815666572005882 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
Alternative 19
Error37.9
Cost584
\[\begin{array}{l} \mathbf{if}\;z \leq -4.3675116054081444 \cdot 10^{+223}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.3624031642850368 \cdot 10^{+123}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.815666572005882 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
Alternative 20
Error35.6
Cost328
\[\begin{array}{l} \mathbf{if}\;z \leq -7.608294193770039 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.815666572005882 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
Alternative 21
Error45.9
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2022297 
(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)))))