Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 14.6 → 5.7

Time: 28.6s

Precision: binary64

Cost: 9804

Math

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

↓

\[\begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x - t_1 \cdot \left(z - y\right)\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{-199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+88}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t_1, x\right)\\ \end{array} \]

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 (/ (- t x) (- a z))) (t_2 (- x (* t_1 (- z y)))))
   (if (<= t_2 -1e-199)
     t_2
     (if (<= t_2 0.0)
       (+ t (/ (- x t) (/ z (- y a))))
       (if (<= t_2 5e+88)
         (+
          (/ (* (- y z) t) (- a z))
          (* x (- (+ (/ z (- a z)) 1.0) (/ y (- a z)))))
         (fma (- y z) t_1 x))))))

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 = (t - x) / (a - z);
	double t_2 = x - (t_1 * (z - y));
	double tmp;
	if (t_2 <= -1e-199) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else if (t_2 <= 5e+88) {
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (a - z))));
	} else {
		tmp = fma((y - z), t_1, x);
	}
	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(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x - Float64(t_1 * Float64(z - y)))
	tmp = 0.0
	if (t_2 <= -1e-199)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	elseif (t_2 <= 5e+88)
		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)))));
	else
		tmp = fma(Float64(y - z), t_1, x);
	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[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(t$95$1 * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-199], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+88], 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], N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.99999999999999982e-200

   1. Initial program 5.7

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

   if -9.99999999999999982e-200 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 57.0

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

   2. Simplified 56.7

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

      [Start] 57.0	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      +-commutative [=>] 57.0	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]
      fma-def [=>] 56.7	\[ \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

   3. Taylor expanded in z around -inf 14.9

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

   4. Simplified 7.5

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

      [Start] 14.9	\[ -1 \cdot \frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z} + t \]
      +-commutative [=>] 14.9	\[ \color{blue}{t + -1 \cdot \frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z}} \]
      mul-1-neg [=>] 14.9	\[ t + \color{blue}{\left(-\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 14.9	\[ \color{blue}{t - \frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z}} \]
      associate-*r* [=>] 14.9	\[ t - \frac{\color{blue}{\left(-1 \cdot a\right) \cdot \left(t - x\right)} + y \cdot \left(t - x\right)}{z} \]
      distribute-rgt-out [=>] 14.9	\[ t - \frac{\color{blue}{\left(t - x\right) \cdot \left(-1 \cdot a + y\right)}}{z} \]
      associate-/l* [=>] 7.5	\[ t - \color{blue}{\frac{t - x}{\frac{z}{-1 \cdot a + y}}} \]
      +-commutative [=>] 7.5	\[ t - \frac{t - x}{\frac{z}{\color{blue}{y + -1 \cdot a}}} \]
      mul-1-neg [=>] 7.5	\[ t - \frac{t - x}{\frac{z}{y + \color{blue}{\left(-a\right)}}} \]

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.99999999999999997e88

   1. Initial program 9.3

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

   2. Taylor expanded in x around -inf 3.6

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

   if 4.99999999999999997e88 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 6.4

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

   2. Simplified 6.4

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

      [Start] 6.4	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      +-commutative [=>] 6.4	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]
      fma-def [=>] 6.4	\[ \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

3. Recombined 4 regimes into one program.

4. Final simplification 5.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq -1 \cdot 10^{-199}:\\ \;\;\;\;x - \frac{t - x}{a - z} \cdot \left(z - y\right)\\ \mathbf{elif}\;x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq 5 \cdot 10^{+88}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	5.7
Cost	4300

\[\begin{array}{l} t_1 := x - \frac{t - x}{a - z} \cdot \left(z - y\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+88}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	6.9
Cost	2633

\[\begin{array}{l} t_1 := x - \frac{t - x}{a - z} \cdot \left(z - y\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-199} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 3
Error	31.8
Cost	1632

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ t_3 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-191}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-115}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+64}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+189}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	35.8
Cost	1505

\[\begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-167}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-163}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-31} \lor \neg \left(z \leq 8.4 \cdot 10^{+43}\right) \land z \leq 4.8 \cdot 10^{+85}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	37.4
Cost	1440

\[\begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+228}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.26 \cdot 10^{+141}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-275}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-286}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-36}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \frac{-a}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	35.9
Cost	1372

\[\begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-163}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+108}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	35.8
Cost	1372

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-167}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-255}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-163}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-48}:\\ \;\;\;\;\frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+55}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+109}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	31.8
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -7 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-148}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+189}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	20.9
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{+172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -65000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-123}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-28}:\\ \;\;\;\;\frac{t - x}{\frac{-z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	21.0
Cost	1368

\[\begin{array}{l} t_1 := \frac{t}{\frac{a - z}{y - z}}\\ t_2 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -3 \cdot 10^{+173}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -40000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-121}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-27}:\\ \;\;\;\;\frac{t - x}{\frac{-z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	18.8
Cost	1364

\[\begin{array}{l} t_1 := t + \frac{y}{z} \cdot \left(x - t\right)\\ t_2 := x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-26}:\\ \;\;\;\;x + z \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+34}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	17.1
Cost	1232

\[\begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -9000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-122}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-36}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-23}:\\ \;\;\;\;\frac{t - x}{\frac{-z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	37.1
Cost	1176

\[\begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{+228}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{+140}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-37}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \frac{-a}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14
Error	34.5
Cost	1176

\[\begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+228}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3 \cdot 10^{+140}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -38000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-54}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \frac{-a}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15
Error	28.8
Cost	1104

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -9 \cdot 10^{+235}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 360000000:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Error	16.0
Cost	1100

\[\begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-41}:\\ \;\;\;\;x + z \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-31}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	36.6
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+17}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-277}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-255}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18
Error	36.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+228}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+141}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{+67}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19
Error	35.8
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+66}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20
Error	45.8
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023066 
(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)))))