Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 14.9 → 7.1

Time: 27.3s

Precision: binary64

Cost: 8904

Math

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

↓

\[\begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-233}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-218}:\\ \;\;\;\;\left(t + \frac{1}{\frac{\frac{z}{t - x}}{a}}\right) + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]

FPCore

(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 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (<= t_1 -1e-233)
     t_1
     (if (<= t_1 5e-218)
       (+ (+ t (/ 1.0 (/ (/ z (- t x)) a))) (* (/ y z) (- x t)))
       (fma (- y z) (/ (- t x) (- a z)) x)))))

C

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 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if (t_1 <= -1e-233) {
		tmp = t_1;
	} else if (t_1 <= 5e-218) {
		tmp = (t + (1.0 / ((z / (t - x)) / a))) + ((y / z) * (x - t));
	} else {
		tmp = fma((y - z), ((t - x) / (a - z)), x);
	}
	return tmp;
}

Julia

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 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e-233)
		tmp = t_1;
	elseif (t_1 <= 5e-218)
		tmp = Float64(Float64(t + Float64(1.0 / Float64(Float64(z / Float64(t - x)) / a))) + Float64(Float64(y / z) * Float64(x - t)));
	else
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x);
	end
	return tmp
end

Wolfram

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[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-233], t$95$1, If[LessEqual[t$95$1, 5e-218], N[(N[(t + N[(1.0 / N[(N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.99999999999999958e-234

   1. Initial program 6.6

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

   if -9.99999999999999958e-234 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5.00000000000000041e-218

   1. Initial program 54.7

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

   2. Simplified 54.4

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

      [Start] 54.7	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      +-commutative [=>] 54.7	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]
      fma-def [=>] 54.4	\[ \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

   3. Taylor expanded in z around inf 17.2

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

   4. Simplified 9.9

      \[\leadsto \color{blue}{\left(t + \frac{a}{z} \cdot \left(t - x\right)\right) - \frac{y}{z} \cdot \left(t - x\right)} \]
      Proof

      [Start] 17.2	\[ -1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \frac{a \cdot \left(t - x\right)}{z}\right) \]
      +-commutative [=>] 17.2	\[ \color{blue}{\left(t + \frac{a \cdot \left(t - x\right)}{z}\right) + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}} \]
      mul-1-neg [=>] 17.2	\[ \left(t + \frac{a \cdot \left(t - x\right)}{z}\right) + \color{blue}{\left(-\frac{y \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 17.2	\[ \color{blue}{\left(t + \frac{a \cdot \left(t - x\right)}{z}\right) - \frac{y \cdot \left(t - x\right)}{z}} \]
      associate-*l/ [<=] 14.5	\[ \left(t + \color{blue}{\frac{a}{z} \cdot \left(t - x\right)}\right) - \frac{y \cdot \left(t - x\right)}{z} \]
      associate-*l/ [<=] 9.9	\[ \left(t + \frac{a}{z} \cdot \left(t - x\right)\right) - \color{blue}{\frac{y}{z} \cdot \left(t - x\right)} \]

   5. Applied egg-rr 9.5

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

   if 5.00000000000000041e-218 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 6.6

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

   2. Simplified 6.6

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

      [Start] 6.6	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      +-commutative [=>] 6.6	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]
      fma-def [=>] 6.6	\[ \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 7.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -1 \cdot 10^{-233}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 5 \cdot 10^{-218}:\\ \;\;\;\;\left(t + \frac{1}{\frac{\frac{z}{t - x}}{a}}\right) + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	7.1
Cost	3017

\[\begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-233} \lor \neg \left(t_1 \leq 5 \cdot 10^{-218}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(t + \frac{1}{\frac{\frac{z}{t - x}}{a}}\right) + \frac{y}{z} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 2
Error	7.2
Cost	2889

\[\begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-233} \lor \neg \left(t_1 \leq 5 \cdot 10^{-218}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(t + \left(t - x\right) \cdot \frac{a}{z}\right) + \frac{y}{z} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 3
Error	7.2
Cost	2633

\[\begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-233} \lor \neg \left(t_1 \leq 5 \cdot 10^{-218}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 4
Error	36.7
Cost	2032

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := t + x \cdot \frac{y}{z}\\ t_3 := t \cdot \left(-\frac{z}{a - z}\right)\\ t_4 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;x \leq -2.35 \cdot 10^{+231}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -0.88:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-50}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -9.3 \cdot 10^{-94}:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-110}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.06 \cdot 10^{-250}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-280}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-245}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4.55 \cdot 10^{-7}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+101}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	27.6
Cost	1760

\[\begin{array}{l} t_1 := t + x \cdot \frac{y}{z}\\ t_2 := \frac{y - z}{a - z}\\ t_3 := x \cdot \left(1 - t_2\right)\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{+229}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+47}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -950000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-46}:\\ \;\;\;\;x - \frac{y - z}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;x \leq 0.245:\\ \;\;\;\;t \cdot t_2\\ \mathbf{elif}\;x \leq 10^{+49}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+174}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - x}{\frac{z}{a - y}}\\ \end{array} \]

Alternative 6
Error	33.1
Cost	1636

\[\begin{array}{l} t_1 := t \cdot \left(-\frac{z}{a - z}\right)\\ t_2 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{+111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-119}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 11500:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+74}:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+209}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	18.0
Cost	1629

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := x - \frac{y - z}{a} \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-75}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-119}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 9200000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+59}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+104} \lor \neg \left(a \leq 1.6 \cdot 10^{+209}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	21.3
Cost	1501

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := t + x \cdot \frac{y}{z}\\ t_3 := x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{+120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 420000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+73}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+176} \lor \neg \left(z \leq 9.2 \cdot 10^{+241}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	16.8
Cost	1496

\[\begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ t_2 := \frac{y - z}{a}\\ t_3 := x - t_2 \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -8.8 \cdot 10^{+108}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -17000000:\\ \;\;\;\;x + t \cdot t_2\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 21000000000000:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 6.9 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Error	34.3
Cost	1372

\[\begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-122}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-6}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+74}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+194}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+209}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	32.0
Cost	1372

\[\begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-119}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+14}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+74}:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{elif}\;a \leq 1.66 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+194}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+209}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	33.0
Cost	1372

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -3900000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-119}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 18:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+74}:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+194}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+208}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	17.4
Cost	1369

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := t + x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-86}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+180} \lor \neg \left(z \leq 9.5 \cdot 10^{+238}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 14
Error	22.5
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + t \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-233}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+109}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+209}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	36.6
Cost	1244

\[\begin{array}{l} \mathbf{if}\;a \leq -1.16 \cdot 10^{+20}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-122}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 0.00145:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+74}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+194}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+214}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Error	38.5
Cost	1240

\[\begin{array}{l} \mathbf{if}\;a \leq -20000000000000:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-122}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-6}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+74}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+194}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \end{array} \]

Alternative 17
Error	27.8
Cost	1108

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := t + x \cdot \frac{y}{z}\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+232}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.85 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4100:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	31.4
Cost	976

\[\begin{array}{l} t_1 := t - y \cdot \frac{t}{z}\\ t_2 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -6.6 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 19000:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 19
Error	35.9
Cost	592

\[\begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+18}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-122}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-6}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+74}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20
Error	35.4
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -17000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+74}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21
Error	45.3
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023057 
(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)))))