Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.8% → 93.8%

Time: 39.6s

Precision: binary64

Cost: 8905

Math

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

↓

\[\begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ t_2 := \left(x - t\right) \cdot \frac{y - a}{z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-276} \lor \neg \left(t_1 \leq 5 \cdot 10^{-229}\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(t_2 + t_2 \cdot \frac{a}{z}\right)\\ \end{array} \]

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 (* (- y z) (/ (- x t) (- a z)))))
        (t_2 (* (- x t) (/ (- y a) z))))
   (if (or (<= t_1 -1e-276) (not (<= t_1 5e-229)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (+ t (+ t_2 (* t_2 (/ a 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 t_2 = (x - t) * ((y - a) / z);
	double tmp;
	if ((t_1 <= -1e-276) || !(t_1 <= 5e-229)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t + (t_2 + (t_2 * (a / 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))))
	t_2 = Float64(Float64(x - t) * Float64(Float64(y - a) / z))
	tmp = 0.0
	if ((t_1 <= -1e-276) || !(t_1 <= 5e-229))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t + Float64(t_2 + Float64(t_2 * Float64(a / 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]}, Block[{t$95$2 = N[(N[(x - t), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-276], N[Not[LessEqual[t$95$1, 5e-229]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(t + N[(t$95$2 + N[(t$95$2 * N[(a / z), $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)))) < -1e-276 or 5.00000000000000016e-229 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.8%

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

   2. Simplified 95.4%

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

      [Start] 91.8	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      +-commutative [=>] 91.8	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]
      associate-*r/ [=>] 72.9	\[ \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} + x \]
      *-commutative [=>] 72.9	\[ \frac{\color{blue}{\left(t - x\right) \cdot \left(y - z\right)}}{a - z} + x \]
      associate-*r/ [<=] 95.4	\[ \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} + x \]
      fma-def [=>] 95.4	\[ \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]

   if -1e-276 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5.00000000000000016e-229

   1. Initial program 5.1%

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

   2. Simplified 11.4%

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

      [Start] 5.1	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      +-commutative [=>] 5.1	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]
      associate-*r/ [=>] 9.8	\[ \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} + x \]
      *-commutative [=>] 9.8	\[ \frac{\color{blue}{\left(t - x\right) \cdot \left(y - z\right)}}{a - z} + x \]
      associate-*r/ [<=] 11.4	\[ \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} + x \]
      fma-def [=>] 11.4	\[ \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]

   3. Taylor expanded in z around inf 77.0%

      \[\leadsto \color{blue}{\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}} + \left(\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t\right)} \]

   4. Simplified 100.0%

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

      [Start] 77.0	\[ \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}} + \left(\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t\right) \]
      associate-+r+ [=>] 77.0	\[ \color{blue}{\left(\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}} + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}\right) + t} \]
      +-commutative [=>] 77.0	\[ \color{blue}{t + \left(\frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}} + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}\right)} \]

3. Recombined 2 regimes into one program.

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq -1 \cdot 10^{-276} \lor \neg \left(x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq 5 \cdot 10^{-229}\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(\left(x - t\right) \cdot \frac{y - a}{z} + \left(\left(x - t\right) \cdot \frac{y - a}{z}\right) \cdot \frac{a}{z}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	90.1%
Cost	3401

\[\begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ t_2 := \left(x - t\right) \cdot \frac{y - a}{z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-150} \lor \neg \left(t_1 \leq 5 \cdot 10^{-229}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \left(t_2 + t_2 \cdot \frac{a}{z}\right)\\ \end{array} \]

Alternative 2
Accuracy	90.1%
Cost	2633

\[\begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-150} \lor \neg \left(t_1 \leq 5 \cdot 10^{-229}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \left(x - t\right) \cdot \frac{y - a}{z}\\ \end{array} \]

Alternative 3
Accuracy	60.4%
Cost	2160

\[\begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y}}\\ t_2 := \frac{t}{\frac{a - z}{y - z}}\\ t_3 := t + \left(x - t\right) \cdot \frac{y - a}{z}\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-8}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-104}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-130}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-100}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-87}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+41}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Accuracy	60.7%
Cost	2160

\[\begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y}}\\ t_2 := \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;t \leq -8 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-9}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-102}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-126}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-101}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-87}:\\ \;\;\;\;t + \left(x - t\right) \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+41}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Accuracy	43.1%
Cost	2097

\[\begin{array}{l} t_1 := \frac{-t}{\frac{z}{y - z}}\\ t_2 := x + \frac{y \cdot t}{a}\\ t_3 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -2.55 \cdot 10^{+184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{+131}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{+83}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-104}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-216}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{\frac{a - z}{-x}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-32} \lor \neg \left(t \leq 5.5 \cdot 10^{+41}\right) \land t \leq 1.7 \cdot 10^{+94}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Accuracy	31.0%
Cost	2036

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a}\\ t_2 := t \cdot \frac{y}{a - z}\\ t_3 := y \cdot \frac{x}{z}\\ \mathbf{if}\;x \leq -1 \cdot 10^{+184}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-36}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-107}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq -3.05 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{-246}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-271}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+167}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+182}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+247}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Accuracy	61.8%
Cost	2024

\[\begin{array}{l} t_1 := \frac{a - z}{y - z}\\ t_2 := x - \frac{x}{t_1}\\ t_3 := \frac{t}{t_1}\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+36}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -4 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-8}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq -5.3 \cdot 10^{-36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-101}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-296}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-157}:\\ \;\;\;\;t + \left(x - t\right) \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+41}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 8
Accuracy	61.6%
Cost	2024

\[\begin{array}{l} t_1 := \frac{a - z}{y - z}\\ t_2 := x - \frac{x}{t_1}\\ t_3 := \frac{t}{t_1}\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+36}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -4 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-7}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-100}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-295}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-158}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+41}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 9
Accuracy	60.3%
Cost	1897

\[\begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y}}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ t_3 := t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-5}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-101}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-269}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-153}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-29} \lor \neg \left(t \leq 5.5 \cdot 10^{+41}\right) \land t \leq 2.8 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Accuracy	30.0%
Cost	1772

\[\begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-28}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-269}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 10^{-192}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+179}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+247}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Accuracy	30.0%
Cost	1772

\[\begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-28}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-274}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-197}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 10^{+169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+182}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+247}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Accuracy	40.5%
Cost	1636

\[\begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-216}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+90}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13
Accuracy	68.4%
Cost	1501

\[\begin{array}{l} t_1 := t - \frac{t - x}{\frac{z}{y}}\\ t_2 := x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+53}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -6.9 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+84} \lor \neg \left(a \leq 1.05 \cdot 10^{+106}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \]

Alternative 14
Accuracy	68.4%
Cost	1501

\[\begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.1 \cdot 10^{+56}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+53}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -8.4 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-96}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+84} \lor \neg \left(a \leq 8.8 \cdot 10^{+104}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \]

Alternative 15
Accuracy	58.2%
Cost	1305

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := y \cdot \frac{-x}{a - z}\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+170}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+184}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+247} \lor \neg \left(x \leq 2.75 \cdot 10^{+280}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Accuracy	58.3%
Cost	1305

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := y \cdot \frac{-x}{a - z}\\ \mathbf{if}\;x \leq -2.95 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+60}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 5.9 \cdot 10^{+169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+184}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+247} \lor \neg \left(x \leq 1.42 \cdot 10^{+281}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Accuracy	58.2%
Cost	1305

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := y \cdot \frac{-x}{a - z}\\ \mathbf{if}\;x \leq -7 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+60}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+170}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+187}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+247} \lor \neg \left(x \leq 5.5 \cdot 10^{+280}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Accuracy	49.5%
Cost	1240

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{+107}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-224}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+90}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+104}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19
Accuracy	38.4%
Cost	1112

\[\begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-148}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-203}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-134}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20
Accuracy	36.8%
Cost	980

\[\begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-146}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -7.1 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-224}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-54}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21
Accuracy	52.3%
Cost	976

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -8 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-296}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 22
Accuracy	51.9%
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-231}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-296}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+100}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 23
Accuracy	55.4%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+43} \lor \neg \left(z \leq 5.3 \cdot 10^{+104}\right):\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 24
Accuracy	38.4%
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 25
Accuracy	25.7%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023160 
(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)))))