Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 14.8 → 6.8

Time: 25.2s

Precision: binary64

Cost: 9804

Math

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

↓

\[\begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-248}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;t_1 \leq 10^{+291}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

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 (* (- y z) (/ (- x t) (- a z))))))
   (if (<= t_1 -5e-219)
     t_1
     (if (<= t_1 2e-248)
       (+ t (/ (- x t) (/ z (- y a))))
       (if (<= t_1 1e+291)
         (fma (- y z) (/ (- t x) (- a z)) x)
         (+ x (/ t (/ (- a z) (- y z)))))))))

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 - ((y - z) * ((x - t) / (a - z)));
	double tmp;
	if (t_1 <= -5e-219) {
		tmp = t_1;
	} else if (t_1 <= 2e-248) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else if (t_1 <= 1e+291) {
		tmp = fma((y - z), ((t - x) / (a - z)), x);
	} else {
		tmp = x + (t / ((a - z) / (y - z)));
	}
	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(y - z) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -5e-219)
		tmp = t_1;
	elseif (t_1 <= 2e-248)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	elseif (t_1 <= 1e+291)
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x);
	else
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / Float64(y - z))));
	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[(y - z), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-219], t$95$1, If[LessEqual[t$95$1, 2e-248], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+291], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.0000000000000002e-219

   1. Initial program 6.7

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

   if -5.0000000000000002e-219 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.99999999999999996e-248

   1. Initial program 54.8

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

   2. Simplified 54.5

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

      [Start] 54.8	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      +-commutative [=>] 54.8	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]
      fma-def [=>] 54.5	\[ \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

   3. Taylor expanded in z around -inf 17.1

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

   4. Simplified 9.6

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

      [Start] 17.1	\[ -1 \cdot \frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z} + t \]
      +-commutative [=>] 17.1	\[ \color{blue}{t + -1 \cdot \frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z}} \]
      mul-1-neg [=>] 17.1	\[ t + \color{blue}{\left(-\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 17.1	\[ \color{blue}{t - \frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z}} \]
      associate-*r* [=>] 17.1	\[ t - \frac{\color{blue}{\left(-1 \cdot a\right) \cdot \left(t - x\right)} + y \cdot \left(t - x\right)}{z} \]
      distribute-rgt-out [=>] 17.1	\[ t - \frac{\color{blue}{\left(t - x\right) \cdot \left(-1 \cdot a + y\right)}}{z} \]
      associate-/l* [=>] 9.6	\[ t - \color{blue}{\frac{t - x}{\frac{z}{-1 \cdot a + y}}} \]
      +-commutative [=>] 9.6	\[ t - \frac{t - x}{\frac{z}{\color{blue}{y + -1 \cdot a}}} \]
      mul-1-neg [=>] 9.6	\[ t - \frac{t - x}{\frac{z}{y + \color{blue}{\left(-a\right)}}} \]

   if 1.99999999999999996e-248 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.9999999999999996e290

   1. Initial program 4.8

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

   2. Simplified 4.8

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

      [Start] 4.8	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      +-commutative [=>] 4.8	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]
      fma-def [=>] 4.8	\[ \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

   if 9.9999999999999996e290 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 28.8

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

   2. Taylor expanded in t around inf 34.1

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

   3. Simplified 17.5

      \[\leadsto x + \color{blue}{\frac{t}{\frac{a - z}{y - z}}} \]
      Proof

      [Start] 34.1	\[ x + \frac{t \cdot \left(y - z\right)}{a - z} \]
      associate-/l* [=>] 17.5	\[ x + \color{blue}{\frac{t}{\frac{a - z}{y - z}}} \]

3. Recombined 4 regimes into one program.

4. Final simplification 6.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq -5 \cdot 10^{-219}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq 2 \cdot 10^{-248}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq 10^{+291}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternatives

Alternative 1
Error	6.8
Cost	3532

\[\begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-248}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;t_1 \leq 10^{+291}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 2
Error	25.9
Cost	1764

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := t + y \cdot \frac{x}{z}\\ t_3 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+193}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+75}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq -7800000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.82 \cdot 10^{-65}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-216}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.06 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-183}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 3
Error	25.4
Cost	1632

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+193}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{+73}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-213}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-183}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	22.1
Cost	1632

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.85 \cdot 10^{+193}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-149}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+27}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	22.8
Cost	1632

\[\begin{array}{l} t_1 := \frac{y - z}{a - z}\\ t_2 := t \cdot t_1\\ t_3 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_4 := x \cdot \left(1 - t_1\right)\\ \mathbf{if}\;a \leq -1.38 \cdot 10^{+193}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3 \cdot 10^{+46}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.82 \cdot 10^{-65}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-150}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+25}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Error	29.2
Cost	1504

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{+20}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-278}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-285}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-194}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \frac{-y}{a - z}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	23.6
Cost	1500

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+193}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -33000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.82 \cdot 10^{-65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-184}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	14.8
Cost	1364

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-149}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+65}:\\ \;\;\;\;t - a \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+95}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	29.0
Cost	1240

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -8 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq -1.82 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-278}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-285}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 4.15 \cdot 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	36.5
Cost	1112

\[\begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-66}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-279}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-285}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-51}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+133}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+176}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Error	26.1
Cost	976

\[\begin{array}{l} t_1 := t + y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-72}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \frac{-y}{a - z}\\ \mathbf{elif}\;z \leq 750000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	15.8
Cost	969

\[\begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-66} \lor \neg \left(a \leq 2.9 \cdot 10^{-149}\right):\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]

Alternative 13
Error	33.1
Cost	844

\[\begin{array}{l} t_1 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-33}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	33.1
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+113}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-30}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 15
Error	27.8
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+50} \lor \neg \left(z \leq 0.0076\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 16
Error	34.5
Cost	460

\[\begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+118}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-32}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17
Error	35.1
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+100}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18
Error	45.2
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023023 
(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)))))