Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Accuracy: 76.8% → 91.2%

Time: 38.9s

Precision: binary64

Cost: 20932

Math

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

↓

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ t_2 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ t_3 := \left(y - z\right) \cdot \left(t - x\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(\sqrt{x}, \sqrt{x}, \frac{t_3}{a - z}\right)\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 10^{-272}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;t_2 \leq 10^{-94}:\\ \;\;\;\;x + \frac{1}{a - z} \cdot t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 (fma (- y z) (/ (- t x) (- a z)) x))
        (t_2 (+ x (* (- z y) (/ (- x t) (- a z)))))
        (t_3 (* (- y z) (- t x))))
   (if (<= t_2 (- INFINITY))
     (fma (sqrt x) (sqrt x) (/ t_3 (- a z)))
     (if (<= t_2 -5e-294)
       t_1
       (if (<= t_2 1e-272)
         (+ t (/ (- x t) (/ z (- y a))))
         (if (<= t_2 1e-94) (+ x (* (/ 1.0 (- a z)) t_3)) t_1))))))

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 = fma((y - z), ((t - x) / (a - z)), x);
	double t_2 = x + ((z - y) * ((x - t) / (a - z)));
	double t_3 = (y - z) * (t - x);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = fma(sqrt(x), sqrt(x), (t_3 / (a - z)));
	} else if (t_2 <= -5e-294) {
		tmp = t_1;
	} else if (t_2 <= 1e-272) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else if (t_2 <= 1e-94) {
		tmp = x + ((1.0 / (a - z)) * t_3);
	} else {
		tmp = t_1;
	}
	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 = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	t_3 = Float64(Float64(y - z) * Float64(t - x))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = fma(sqrt(x), sqrt(x), Float64(t_3 / Float64(a - z)));
	elseif (t_2 <= -5e-294)
		tmp = t_1;
	elseif (t_2 <= 1e-272)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	elseif (t_2 <= 1e-94)
		tmp = Float64(x + Float64(Float64(1.0 / Float64(a - z)) * t_3));
	else
		tmp = t_1;
	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[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $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]}, Block[{t$95$3 = N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[Sqrt[x], $MachinePrecision] * N[Sqrt[x], $MachinePrecision] + N[(t$95$3 / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-294], t$95$1, If[LessEqual[t$95$2, 1e-272], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-94], N[(x + N[(N[(1.0 / N[(a - z), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0

   1. Initial program 0.0%

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

   2. Simplified 86.2%

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

      [Start] 0.0	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      associate-*r/ [=>] 86.2	\[ x + \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} \]

   3. Applied egg-rr 41.1%

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

      [Start] 86.2	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      add-sqr-sqrt [=>] 41.0	\[ \color{blue}{\sqrt{x} \cdot \sqrt{x}} + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      fma-def [=>] 41.2	\[ \color{blue}{\mathsf{fma}\left(\sqrt{x}, \sqrt{x}, \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\right)} \]
      *-commutative [=>] 41.2	\[ \mathsf{fma}\left(\sqrt{x}, \sqrt{x}, \frac{\color{blue}{\left(t - x\right) \cdot \left(y - z\right)}}{a - z}\right) \]
      *-un-lft-identity [=>] 41.2	\[ \mathsf{fma}\left(\sqrt{x}, \sqrt{x}, \frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{1 \cdot \left(a - z\right)}}\right) \]
      times-frac [=>] 41.1	\[ \mathsf{fma}\left(\sqrt{x}, \sqrt{x}, \color{blue}{\frac{t - x}{1} \cdot \frac{y - z}{a - z}}\right) \]
      flip-- [=>] 5.3	\[ \mathsf{fma}\left(\sqrt{x}, \sqrt{x}, \frac{\color{blue}{\frac{t \cdot t - x \cdot x}{t + x}}}{1} \cdot \frac{y - z}{a - z}\right) \]
      associate-/l/ [=>] 5.3	\[ \mathsf{fma}\left(\sqrt{x}, \sqrt{x}, \color{blue}{\frac{t \cdot t - x \cdot x}{1 \cdot \left(t + x\right)}} \cdot \frac{y - z}{a - z}\right) \]
      *-un-lft-identity [<=] 5.3	\[ \mathsf{fma}\left(\sqrt{x}, \sqrt{x}, \frac{t \cdot t - x \cdot x}{\color{blue}{t + x}} \cdot \frac{y - z}{a - z}\right) \]
      flip-- [<=] 41.1	\[ \mathsf{fma}\left(\sqrt{x}, \sqrt{x}, \color{blue}{\left(t - x\right)} \cdot \frac{y - z}{a - z}\right) \]

   4. Simplified 41.2%

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

      [Start] 41.1	\[ \mathsf{fma}\left(\sqrt{x}, \sqrt{x}, \left(t - x\right) \cdot \frac{y - z}{a - z}\right) \]
      associate-*r/ [=>] 41.2	\[ \mathsf{fma}\left(\sqrt{x}, \sqrt{x}, \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}}\right) \]

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.0000000000000003e-294 or 9.9999999999999996e-95 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.9%

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

   2. Simplified 91.9%

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

      [Start] 91.9	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      +-commutative [=>] 91.9	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]
      fma-def [=>] 91.9	\[ \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

   if -5.0000000000000003e-294 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.9999999999999993e-273

   1. Initial program 6.5%

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

   2. Simplified 7.0%

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

      [Start] 6.5	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      +-commutative [=>] 6.5	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]
      fma-def [=>] 7.0	\[ \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

   3. Taylor expanded in z around -inf 79.9%

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

   4. Simplified 93.7%

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

      [Start] 79.9	\[ -1 \cdot \frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z} + t \]
      +-commutative [=>] 79.9	\[ \color{blue}{t + -1 \cdot \frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z}} \]
      mul-1-neg [=>] 79.9	\[ t + \color{blue}{\left(-\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 79.9	\[ \color{blue}{t - \frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z}} \]
      associate-*r* [=>] 79.9	\[ t - \frac{\color{blue}{\left(-1 \cdot a\right) \cdot \left(t - x\right)} + y \cdot \left(t - x\right)}{z} \]
      distribute-rgt-out [=>] 79.9	\[ t - \frac{\color{blue}{\left(t - x\right) \cdot \left(-1 \cdot a + y\right)}}{z} \]
      associate-/l* [=>] 93.7	\[ t - \color{blue}{\frac{t - x}{\frac{z}{-1 \cdot a + y}}} \]
      +-commutative [=>] 93.7	\[ t - \frac{t - x}{\frac{z}{\color{blue}{y + -1 \cdot a}}} \]
      mul-1-neg [=>] 93.7	\[ t - \frac{t - x}{\frac{z}{y + \color{blue}{\left(-a\right)}}} \]

   if 9.9999999999999993e-273 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.9999999999999996e-95

   1. Initial program 70.9%

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

   2. Simplified 86.5%

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

      [Start] 70.9	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      associate-*r/ [=>] 86.5	\[ x + \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} \]

   3. Applied egg-rr 86.3%

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

      [Start] 86.5	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      div-inv [=>] 86.3	\[ x + \color{blue}{\left(\left(y - z\right) \cdot \left(t - x\right)\right) \cdot \frac{1}{a - z}} \]
      *-commutative [=>] 86.3	\[ x + \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} \]

3. Recombined 4 regimes into one program.

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(\sqrt{x}, \sqrt{x}, \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\right)\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -5 \cdot 10^{-294}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 10^{-272}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 10^{-94}:\\ \;\;\;\;x + \frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	91.7%
Cost	10704

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - x\right)\\ t_2 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ t_3 := \mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;x + \frac{t_1}{a - z}\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-294}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 10^{-272}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;t_2 \leq 10^{-94}:\\ \;\;\;\;x + \frac{1}{a - z} \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Accuracy	91.7%
Cost	4560

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - x\right)\\ t_2 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;x + \frac{t_1}{a - z}\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-294}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 10^{-272}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;t_2 \leq 10^{-94}:\\ \;\;\;\;x + \frac{1}{a - z} \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	92.1%
Cost	4432

\[\begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ t_2 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-294}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;t_2 \leq 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Accuracy	90.6%
Cost	3533

\[\begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-294} \lor \neg \left(t_1 \leq 10^{-272}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 5
Accuracy	49.9%
Cost	2033

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-28}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-32}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-196}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -3.35 \cdot 10^{-223}:\\ \;\;\;\;\frac{x + t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-186}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-134}:\\ \;\;\;\;\frac{-y}{\frac{a - z}{x}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-50}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 33000:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+27} \lor \neg \left(a \leq 5.4 \cdot 10^{+57}\right) \land a \leq 1.25 \cdot 10^{+157}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Accuracy	50.3%
Cost	1900

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-28}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq -3.85 \cdot 10^{-32}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-195}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{-223}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-185}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-134}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-54}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-6}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;a \leq 2600:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+157}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	50.1%
Cost	1900

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -6.8 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-28}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq -1.32 \cdot 10^{-33}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-197}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-223}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-185}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-49}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 0.00013:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;a \leq 9500:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+157}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	50.1%
Cost	1900

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-28}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-197}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -3.15 \cdot 10^{-223}:\\ \;\;\;\;\frac{x + t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-187}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-134}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-49}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 0.00043:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;a \leq 2600:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+157}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Accuracy	51.3%
Cost	1764

\[\begin{array}{l} t_1 := x - \frac{z \cdot t}{a}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ t_3 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;y \leq -2.65 \cdot 10^{+203}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+183}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-52}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-92}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-131}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+85}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Accuracy	50.7%
Cost	1636

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-28}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-32}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-196}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-223}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-189}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-89}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+157}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Accuracy	53.6%
Cost	1636

\[\begin{array}{l} t_1 := \frac{-t}{\frac{z}{y - z}}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-223}:\\ \;\;\;\;\frac{x + t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-134}:\\ \;\;\;\;\frac{-y}{\frac{a - z}{x}}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 0.14:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;a \leq 170000000:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+157}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Accuracy	53.3%
Cost	1636

\[\begin{array}{l} t_1 := \frac{-t}{\frac{z}{y - z}}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -4.4 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-223}:\\ \;\;\;\;\frac{x + t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-134}:\\ \;\;\;\;\frac{-y}{\frac{a - z}{x}}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-31}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;a \leq 1450000:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a - z}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+157}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Accuracy	60.2%
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -1.82 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.66 \cdot 10^{-223}:\\ \;\;\;\;\frac{x + t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-134}:\\ \;\;\;\;\frac{-y}{\frac{a - z}{x}}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Accuracy	62.3%
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -2 \cdot 10^{+45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.35 \cdot 10^{-223}:\\ \;\;\;\;\frac{x + t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-134}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Accuracy	63.0%
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -1.72 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-223}:\\ \;\;\;\;\frac{x + t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-134}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 16
Accuracy	45.1%
Cost	1116

\[\begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+221}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-81}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-185}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-134}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-91}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+178}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Accuracy	45.2%
Cost	1116

\[\begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+221}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{+141}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-84}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-185}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-87}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+178}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Accuracy	69.3%
Cost	1104

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{+45}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 10^{-127}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 19
Accuracy	69.0%
Cost	1104

\[\begin{array}{l} \mathbf{if}\;a \leq -1.22 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-177}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-56}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+118}:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 20
Accuracy	77.1%
Cost	1100

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-86}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 21
Accuracy	78.1%
Cost	1100

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-84}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 22
Accuracy	77.7%
Cost	969

\[\begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{-112} \lor \neg \left(a \leq 3.2 \cdot 10^{-86}\right):\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \]

Alternative 23
Accuracy	43.9%
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -6.7 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-269}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-80}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+117}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 24
Accuracy	44.4%
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 25
Accuracy	29.5%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023135 
(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)))))