Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 23.59% → 4.31%

Time: 32.4s

Precision: binary64

Cost: 9417

Math

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

↓

\[\begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-274} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(1 + \frac{z - y}{a - z}, x, \frac{t}{\frac{a - z}{y - z}}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

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 (or (<= t_1 -4e-274) (not (<= t_1 0.0)))
     (fma (+ 1.0 (/ (- z y) (- a z))) x (/ t (/ (- a z) (- y z))))
     (+ t (/ (- x t) (/ z (- y a)))))))

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 <= -4e-274) || !(t_1 <= 0.0)) {
		tmp = fma((1.0 + ((z - y) / (a - z))), x, (t / ((a - z) / (y - z))));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	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 <= -4e-274) || !(t_1 <= 0.0))
		tmp = fma(Float64(1.0 + Float64(Float64(z - y) / Float64(a - z))), x, Float64(t / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	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[Or[LessEqual[t$95$1, -4e-274], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(1.0 + N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x + N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -3.99999999999999986e-274 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 11.87

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

   2. Taylor expanded in x around 0 22.14

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

   3. Simplified 4.27

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

      [Start] 22.14	\[ \left(1 + -1 \cdot \frac{y - z}{a - z}\right) \cdot x + \frac{t \cdot \left(y - z\right)}{a - z} \]
      fma-def [=>] 22.14	\[ \color{blue}{\mathsf{fma}\left(1 + -1 \cdot \frac{y - z}{a - z}, x, \frac{t \cdot \left(y - z\right)}{a - z}\right)} \]
      mul-1-neg [=>] 22.14	\[ \mathsf{fma}\left(1 + \color{blue}{\left(-\frac{y - z}{a - z}\right)}, x, \frac{t \cdot \left(y - z\right)}{a - z}\right) \]
      associate-/l* [=>] 4.27	\[ \mathsf{fma}\left(1 + \left(-\frac{y - z}{a - z}\right), x, \color{blue}{\frac{t}{\frac{a - z}{y - z}}}\right) \]

   if -3.99999999999999986e-274 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 95.11

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

   2. Simplified 94.75

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

      [Start] 95.11	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      +-commutative [=>] 95.11	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]
      fma-def [=>] 94.75	\[ \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

   3. Taylor expanded in z around -inf 18.9

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

   4. Simplified 4.52

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

      [Start] 18.9	\[ -1 \cdot \frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z} + t \]
      +-commutative [=>] 18.9	\[ \color{blue}{t + -1 \cdot \frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z}} \]
      mul-1-neg [=>] 18.9	\[ t + \color{blue}{\left(-\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 18.9	\[ \color{blue}{t - \frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z}} \]
      associate-*r* [=>] 18.9	\[ t - \frac{\color{blue}{\left(-1 \cdot a\right) \cdot \left(t - x\right)} + y \cdot \left(t - x\right)}{z} \]
      distribute-rgt-out [=>] 18.9	\[ t - \frac{\color{blue}{\left(t - x\right) \cdot \left(-1 \cdot a + y\right)}}{z} \]
      associate-/l* [=>] 4.52	\[ t - \color{blue}{\frac{t - x}{\frac{z}{-1 \cdot a + y}}} \]
      +-commutative [=>] 4.52	\[ t - \frac{t - x}{\frac{z}{\color{blue}{y + -1 \cdot a}}} \]
      mul-1-neg [=>] 4.52	\[ t - \frac{t - x}{\frac{z}{y + \color{blue}{\left(-a\right)}}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 4.31

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq -4 \cdot 10^{-274} \lor \neg \left(x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(1 + \frac{z - y}{a - z}, x, \frac{t}{\frac{a - z}{y - z}}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternatives

Alternative 1
Error	8.18%
Cost	10705

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ t_2 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;t_2 \leq 10^{-7} \lor \neg \left(t_2 \leq 10^{+306}\right):\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	8.19%
Cost	4433

\[\begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;t_1 \leq 10^{-7} \lor \neg \left(t_1 \leq 10^{+306}\right):\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	10.93%
Cost	2633

\[\begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-215} \lor \neg \left(t_1 \leq 2 \cdot 10^{-280}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 4
Error	24.09%
Cost	1893

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y - z}}\\ t_2 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -5.9 \cdot 10^{+197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.65 \cdot 10^{-205}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-49} \lor \neg \left(z \leq 9.5 \cdot 10^{+182}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	50.88%
Cost	1636

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -940000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-15}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.62 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-100}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-188}:\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-206}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-269}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-180}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	27.87%
Cost	1629

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;z \leq -3 \cdot 10^{+199}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.65 \cdot 10^{-205}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-49} \lor \neg \left(z \leq 1.02 \cdot 10^{+183}\right):\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	27.42%
Cost	1628

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+198}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-205}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+199}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \]

Alternative 8
Error	44.6%
Cost	1504

\[\begin{array}{l} t_1 := t - a \cdot \frac{x}{z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+81}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+110}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	32.62%
Cost	1500

\[\begin{array}{l} t_1 := t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-64}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 18000000000000:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \left(1 + \frac{z - y}{a - z}\right)\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+256}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \]

Alternative 10
Error	50.62%
Cost	1372

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -4200000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-17}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-99}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-270}:\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-177}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-16}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	50.78%
Cost	1372

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -220000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-19}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-99}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-271}:\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-181}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-10}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	49.65%
Cost	1304

\[\begin{array}{l} t_1 := t \cdot \frac{-z}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -2800000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-206}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-270}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-156}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	54.37%
Cost	1240

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+204}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-27}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14
Error	48.61%
Cost	1240

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -21500000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-190}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-206}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-270}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-180}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+48}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	35.15%
Cost	1236

\[\begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+251}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \]

Alternative 16
Error	35.19%
Cost	1236

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-64}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+251}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \]

Alternative 17
Error	39.73%
Cost	1104

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-206}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Error	56.09%
Cost	976

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-271}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-260}:\\ \;\;\;\;\frac{-y}{\frac{z}{t}}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	55.11%
Cost	976

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-271}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-161}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-28}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 20
Error	31.72%
Cost	972

\[\begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+128}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.8:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 21
Error	58.68%
Cost	780

\[\begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+128}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-271}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{-260}:\\ \;\;\;\;\frac{-y}{\frac{z}{t}}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22
Error	56.4%
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+128}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 23
Error	71.37%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023121 
(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)))))