Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.3% → 96.1%

Time: 21.5s

Precision: binary64

Cost: 10704

Math

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

↓

\[\begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ t_2 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;t_2 \leq 0.5:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{+286}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 (- t x) (/ (- y z) (- a z)) x))
        (t_2 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (<= t_2 -1e-293)
     t_1
     (if (<= t_2 0.0)
       (+ t (* (/ x z) (- y a)))
       (if (<= t_2 0.5)
         (+
          (/ (* (- y z) t) (- a z))
          (* x (- (+ (/ z (- a z)) 1.0) (/ y (- a z)))))
         (if (<= t_2 4e+286) (fma (- y z) (/ (- t x) (- a z)) x) 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((t - x), ((y - z) / (a - z)), x);
	double t_2 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if (t_2 <= -1e-293) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + ((x / z) * (y - a));
	} else if (t_2 <= 0.5) {
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (a - z))));
	} else if (t_2 <= 4e+286) {
		tmp = fma((y - z), ((t - x) / (a - z)), x);
	} 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(t - x), Float64(Float64(y - z) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -1e-293)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(x / z) * Float64(y - a)));
	elseif (t_2 <= 0.5)
		tmp = Float64(Float64(Float64(Float64(y - z) * t) / Float64(a - z)) + Float64(x * Float64(Float64(Float64(z / Float64(a - z)) + 1.0) - Float64(y / Float64(a - z)))));
	elseif (t_2 <= 4e+286)
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x);
	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[(t - x), $MachinePrecision] * N[(N[(y - z), $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]}, If[LessEqual[t$95$2, -1e-293], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(x / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.5], N[(N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+286], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $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)))) < -1.0000000000000001e-293 or 4.00000000000000013e286 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.5%

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

   2. Simplified 96.3%

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

      [Start] 90.5%	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      +-commutative [=>] 90.5%	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]
      associate-*r/ [=>] 76.4%	\[ \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} + x \]
      *-commutative [=>] 76.4%	\[ \frac{\color{blue}{\left(t - x\right) \cdot \left(y - z\right)}}{a - z} + x \]
      associate-*r/ [<=] 96.2%	\[ \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} + x \]
      fma-def [=>] 96.3%	\[ \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]

   if -1.0000000000000001e-293 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

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

   2. Taylor expanded in z around inf 81.4%

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

   3. Simplified 81.4%

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

      [Start] 81.4%	\[ \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + t\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      +-commutative [=>] 81.4%	\[ \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right)} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      associate--l+ [=>] 81.4%	\[ \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]
      associate-*r/ [=>] 81.4%	\[ t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]
      associate-*r/ [=>] 81.4%	\[ t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]
      div-sub [<=] 81.4%	\[ t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]
      distribute-lft-out-- [=>] 81.4%	\[ t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]
      mul-1-neg [=>] 81.4%	\[ t + \frac{\color{blue}{-\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]
      distribute-neg-frac [<=] 81.4%	\[ t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 81.4%	\[ \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
      distribute-rgt-out-- [=>] 81.4%	\[ t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

   4. Taylor expanded in t around 0 81.4%

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

   5. Simplified 99.8%

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

      [Start] 81.4%	\[ t - -1 \cdot \frac{\left(y - a\right) \cdot x}{z} \]
      associate-*r/ [=>] 81.4%	\[ t - \color{blue}{\frac{-1 \cdot \left(\left(y - a\right) \cdot x\right)}{z}} \]
      mul-1-neg [=>] 81.4%	\[ t - \frac{\color{blue}{-\left(y - a\right) \cdot x}}{z} \]
      *-commutative [=>] 81.4%	\[ t - \frac{-\color{blue}{x \cdot \left(y - a\right)}}{z} \]
      distribute-rgt-neg-in [=>] 81.4%	\[ t - \frac{\color{blue}{x \cdot \left(-\left(y - a\right)\right)}}{z} \]
      neg-sub0 [=>] 81.4%	\[ t - \frac{x \cdot \color{blue}{\left(0 - \left(y - a\right)\right)}}{z} \]
      associate--r- [=>] 81.4%	\[ t - \frac{x \cdot \color{blue}{\left(\left(0 - y\right) + a\right)}}{z} \]
      neg-sub0 [<=] 81.4%	\[ t - \frac{x \cdot \left(\color{blue}{\left(-y\right)} + a\right)}{z} \]
      distribute-rgt-out [<=] 81.4%	\[ t - \frac{\color{blue}{\left(-y\right) \cdot x + a \cdot x}}{z} \]
      +-commutative [<=] 81.4%	\[ t - \frac{\color{blue}{a \cdot x + \left(-y\right) \cdot x}}{z} \]
      distribute-rgt-out [=>] 81.4%	\[ t - \frac{\color{blue}{x \cdot \left(a + \left(-y\right)\right)}}{z} \]
      sub-neg [<=] 81.4%	\[ t - \frac{x \cdot \color{blue}{\left(a - y\right)}}{z} \]
      *-commutative [=>] 81.4%	\[ t - \frac{\color{blue}{\left(a - y\right) \cdot x}}{z} \]
      associate-*r/ [<=] 99.8%	\[ t - \color{blue}{\left(a - y\right) \cdot \frac{x}{z}} \]

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.5

   1. Initial program 77.9%

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

   2. Taylor expanded in x around -inf 99.5%

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

   if 0.5 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.00000000000000013e286

   1. Initial program 97.9%

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

   2. Simplified 97.9%

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

      [Start] 97.9%	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      +-commutative [=>] 97.9%	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]
      fma-def [=>] 97.9%	\[ \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

3. Recombined 4 regimes into one program.

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -1 \cdot 10^{-293}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0.5:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 4 \cdot 10^{+286}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	96.1%
Cost	10704

\[\begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ t_2 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;t_2 \leq 0.5:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{+286}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	96.0%
Cost	10704

\[\begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ t_2 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;t_2 \leq 0.5:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+232}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Accuracy	93.2%
Cost	4300

\[\begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;t_1 \leq 0.5:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	91.1%
Cost	2633

\[\begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-293} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \end{array} \]

Alternative 5
Accuracy	67.7%
Cost	1632

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+202}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-129}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;z \leq -7.7 \cdot 10^{-205}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+76}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Accuracy	50.9%
Cost	1568

\[\begin{array}{l} t_1 := \frac{t}{\left(--1\right) - \frac{a}{z}}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -1.42 \cdot 10^{+226}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+198}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-258}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{-272}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-185}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-152}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+83}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	49.9%
Cost	1504

\[\begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+226}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-257}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+112}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8
Accuracy	49.1%
Cost	1504

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -7.1 \cdot 10^{+227}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-274}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-152}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 4.15 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9
Accuracy	70.5%
Cost	1496

\[\begin{array}{l} t_1 := t + \frac{x}{z} \cdot \left(y - a\right)\\ t_2 := x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.4 \cdot 10^{+123}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.7 \cdot 10^{-205}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Accuracy	57.8%
Cost	1368

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -75000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-253}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-305}:\\ \;\;\;\;\frac{-x}{\frac{z}{a - y}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Accuracy	69.2%
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := t + x \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{+197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Accuracy	69.1%
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+202}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+76}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Accuracy	52.2%
Cost	1304

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+69}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-274}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-153}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\left(--1\right) - \frac{a}{z}}\\ \end{array} \]

Alternative 14
Accuracy	48.5%
Cost	1240

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{+226}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+74}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-153}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15
Accuracy	73.3%
Cost	1232

\[\begin{array}{l} t_1 := \frac{a}{t - x}\\ t_2 := t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-179}:\\ \;\;\;\;x + \frac{y - z}{t_1}\\ \mathbf{elif}\;z \leq -7.7 \cdot 10^{-205}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{y}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Accuracy	69.5%
Cost	1232

\[\begin{array}{l} t_1 := t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+109}:\\ \;\;\;\;x + \frac{x - t}{-1 + \frac{a}{z}}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-65}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;a \leq 520000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 17
Accuracy	67.8%
Cost	1104

\[\begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-188}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-65}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;a \leq 5200000000000:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \end{array} \]

Alternative 18
Accuracy	36.5%
Cost	976

\[\begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-188}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19
Accuracy	37.0%
Cost	976

\[\begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-240}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1150:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20
Accuracy	37.6%
Cost	848

\[\begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-120}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 340:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+57}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21
Accuracy	61.3%
Cost	841

\[\begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-120} \lor \neg \left(x \leq 8 \cdot 10^{+76}\right):\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 22
Accuracy	61.3%
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-120}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 23
Accuracy	36.5%
Cost	716

\[\begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-188}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+57}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24
Accuracy	38.6%
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+58}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 25
Accuracy	25.4%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023171 
(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)))))