Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 14.6 → 6.0

Time: 27.1s

Precision: binary64

Cost: 9805

Math

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

↓

\[\begin{array}{l} t_1 := x + \frac{x - t}{a - z} \cdot \left(z - y\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-291} \lor \neg \left(t_1 \leq 2 \cdot 10^{-254}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + \left(t - x\right) \cdot \frac{a}{z}\right) + \frac{y}{z} \cdot \left(x - t\right)\\ \end{array} \]

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 (* (/ (- x t) (- a z)) (- z y)))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ (* (- y z) (- t x)) (- a z)))
     (if (or (<= t_1 -2e-291) (not (<= t_1 2e-254)))
       (fma (- y z) (/ (- t x) (- a z)) x)
       (+ (+ t (* (- t x) (/ a z))) (* (/ y z) (- x t)))))))

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 + (((x - t) / (a - z)) * (z - y));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + (((y - z) * (t - x)) / (a - z));
	} else if ((t_1 <= -2e-291) || !(t_1 <= 2e-254)) {
		tmp = fma((y - z), ((t - x) / (a - z)), x);
	} else {
		tmp = (t + ((t - x) * (a / z))) + ((y / z) * (x - t));
	}
	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(Float64(x - t) / Float64(a - z)) * Float64(z - y)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)));
	elseif ((t_1 <= -2e-291) || !(t_1 <= 2e-254))
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x);
	else
		tmp = Float64(Float64(t + Float64(Float64(t - x) * Float64(a / z))) + Float64(Float64(y / z) * Float64(x - t)));
	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[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -2e-291], N[Not[LessEqual[t$95$1, 2e-254]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(t + N[(N[(t - x), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 64.0

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

   2. Simplified 7.2

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

      [Start] 64.0	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      associate-*r/ [=>] 7.2	\[ x + \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} \]

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.99999999999999992e-291 or 1.9999999999999998e-254 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 6.0

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

   2. Simplified 6.0

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

      [Start] 6.0	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      +-commutative [=>] 6.0	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]
      fma-def [=>] 6.0	\[ \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

   if -1.99999999999999992e-291 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.9999999999999998e-254

   1. Initial program 59.0

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

   2. Simplified 58.7

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

      [Start] 59.0	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      +-commutative [=>] 59.0	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]
      fma-def [=>] 58.7	\[ \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

   3. Taylor expanded in z around inf 14.0

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

   4. Simplified 5.5

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

      [Start] 14.0	\[ -1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \frac{a \cdot \left(t - x\right)}{z}\right) \]
      +-commutative [=>] 14.0	\[ \color{blue}{\left(t + \frac{a \cdot \left(t - x\right)}{z}\right) + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}} \]
      mul-1-neg [=>] 14.0	\[ \left(t + \frac{a \cdot \left(t - x\right)}{z}\right) + \color{blue}{\left(-\frac{y \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 14.0	\[ \color{blue}{\left(t + \frac{a \cdot \left(t - x\right)}{z}\right) - \frac{y \cdot \left(t - x\right)}{z}} \]
      associate-*l/ [<=] 10.9	\[ \left(t + \color{blue}{\frac{a}{z} \cdot \left(t - x\right)}\right) - \frac{y \cdot \left(t - x\right)}{z} \]
      associate-*l/ [<=] 5.5	\[ \left(t + \frac{a}{z} \cdot \left(t - x\right)\right) - \color{blue}{\frac{y}{z} \cdot \left(t - x\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 6.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{x - t}{a - z} \cdot \left(z - y\right) \leq -\infty:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{x - t}{a - z} \cdot \left(z - y\right) \leq -2 \cdot 10^{-291} \lor \neg \left(x + \frac{x - t}{a - z} \cdot \left(z - y\right) \leq 2 \cdot 10^{-254}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + \left(t - x\right) \cdot \frac{a}{z}\right) + \frac{y}{z} \cdot \left(x - t\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	6.0
Cost	3789

\[\begin{array}{l} t_1 := x + \frac{x - t}{a - z} \cdot \left(z - y\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-291} \lor \neg \left(t_1 \leq 2 \cdot 10^{-254}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(t + \left(t - x\right) \cdot \frac{a}{z}\right) + \frac{y}{z} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 2
Error	6.5
Cost	3533

\[\begin{array}{l} t_1 := x + \frac{x - t}{a - z} \cdot \left(z - y\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x \cdot \left(1 + \frac{z - y}{a - z}\right)\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-291} \lor \neg \left(t_1 \leq 2 \cdot 10^{-254}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 3
Error	6.0
Cost	3533

\[\begin{array}{l} t_1 := x + \frac{x - t}{a - z} \cdot \left(z - y\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-291} \lor \neg \left(t_1 \leq 2 \cdot 10^{-254}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 4
Error	22.3
Cost	1632

\[\begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a}\\ \mathbf{if}\;a \leq -8 \cdot 10^{+206}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{+128}:\\ \;\;\;\;x + z \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{+76}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-93}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-78}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 270:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]

Alternative 5
Error	25.3
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-84}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	19.3
Cost	1364

\[\begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(1 + \frac{z - y}{a - z}\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-226}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-188}:\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-53}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	21.9
Cost	1236

\[\begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(1 + \frac{z - y}{a - z}\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-226}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-188}:\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-53}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	27.0
Cost	1108

\[\begin{array}{l} t_1 := t + x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+43}:\\ \;\;\;\;x + \frac{x \cdot z}{a}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+187}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	27.1
Cost	1108

\[\begin{array}{l} t_1 := t + x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+32}:\\ \;\;\;\;\frac{-x \cdot y}{a - z}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{x \cdot z}{a}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+182}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	32.8
Cost	976

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+91}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-188}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11
Error	31.1
Cost	976

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-188}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	28.8
Cost	976

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	28.4
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+40}:\\ \;\;\;\;x + \frac{x \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \]

Alternative 14
Error	28.4
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+75}:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 1.68 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{x \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \]

Alternative 15
Error	28.3
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+75}:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+45}:\\ \;\;\;\;x + \frac{x \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \]

Alternative 16
Error	23.4
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+75}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-56}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{x \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \]

Alternative 17
Error	24.2
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+75}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-53}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+33}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+43}:\\ \;\;\;\;x + \frac{x \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \]

Alternative 18
Error	21.6
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+75} \lor \neg \left(z \leq 1.65 \cdot 10^{-53}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 19
Error	35.8
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+92}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-226}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-184}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20
Error	35.8
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+91}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-226}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-188}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 21
Error	35.4
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+93}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 22
Error	46.1
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023016 
(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)))))