Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 14.3 → 3.5

Time: 2.1min

Precision: binary64

Cost: 8904

Math

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

↓

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-306}:\\ \;\;\;\;x - \begin{array}{l} \mathbf{if}\;z - y \ne 0:\\ \;\;\;\;\frac{t - x}{\frac{z - a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - y}{a - z} \cdot \left(t - x\right)\\ \end{array}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;\left(y - a\right) \cdot x \ne 0:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x}}{a - y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - a}{z} \cdot x\\ \end{array} + t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{y - z}{z - a}, x\right)\\ \end{array} \]

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 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -2e-306)
     (-
      x
      (if (!= (- z y) 0.0)
        (/ (- t x) (/ (- z a) (- y z)))
        (* (/ (- z y) (- a z)) (- t x))))
     (if (<= t_1 0.0)
       (+
        (if (!= (* (- y a) x) 0.0)
          (/ -1.0 (/ (/ z x) (- a y)))
          (* (/ (- y a) z) x))
        t)
       (fma (- x t) (/ (- y z) (- z a)) 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 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp_1;
	if (t_1 <= -2e-306) {
		double tmp_2;
		if ((z - y) != 0.0) {
			tmp_2 = (t - x) / ((z - a) / (y - z));
		} else {
			tmp_2 = ((z - y) / (a - z)) * (t - x);
		}
		tmp_1 = x - tmp_2;
	} else if (t_1 <= 0.0) {
		double tmp_3;
		if (((y - a) * x) != 0.0) {
			tmp_3 = -1.0 / ((z / x) / (a - y));
		} else {
			tmp_3 = ((y - a) / z) * x;
		}
		tmp_1 = tmp_3 + t;
	} else {
		tmp_1 = fma((x - t), ((y - z) / (z - a)), x);
	}
	return tmp_1;
}

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(t - x) / Float64(a - z))))
	tmp_1 = 0.0
	if (t_1 <= -2e-306)
		tmp_2 = 0.0
		if (Float64(z - y) != 0.0)
			tmp_2 = Float64(Float64(t - x) / Float64(Float64(z - a) / Float64(y - z)));
		else
			tmp_2 = Float64(Float64(Float64(z - y) / Float64(a - z)) * Float64(t - x));
		end
		tmp_1 = Float64(x - tmp_2);
	elseif (t_1 <= 0.0)
		tmp_3 = 0.0
		if (Float64(Float64(y - a) * x) != 0.0)
			tmp_3 = Float64(-1.0 / Float64(Float64(z / x) / Float64(a - y)));
		else
			tmp_3 = Float64(Float64(Float64(y - a) / z) * x);
		end
		tmp_1 = Float64(tmp_3 + t);
	else
		tmp_1 = fma(Float64(x - t), Float64(Float64(y - z) / Float64(z - a)), x);
	end
	return tmp_1
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[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-306], N[(x - If[Unequal[N[(z - y), $MachinePrecision], 0.0], N[(N[(t - x), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(If[Unequal[N[(N[(y - a), $MachinePrecision] * x), $MachinePrecision], 0.0], N[(-1.0 / N[(N[(z / x), $MachinePrecision] / N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]] + t), $MachinePrecision], N[(N[(x - t), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.00000000000000006e-306

   1. Initial program 7.1

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

   2. Simplified 7.1

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

   3. Applied egg-rr 4.0

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

   4. Applied egg-rr 3.9

      \[\leadsto x - \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;z - y \ne 0:\\ \;\;\;\;\frac{t - x}{\frac{a - z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t - x}{z - a}\\ } \end{array}} \]

   5. Simplified 3.9

      \[\leadsto x - \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;z - y \ne 0:\\ \;\;\;\;\frac{t - x}{\frac{z - a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - y}{a - z} \cdot \left(t - x\right)\\ } \end{array}} \]
      Proof

   if -2.00000000000000006e-306 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 61.8

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

   2. Taylor expanded in z around inf 11.0

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

   3. Simplified 11.0

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

   4. Taylor expanded in t around 0 11.0

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

   5. Simplified 11.0

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

   6. Applied egg-rr 0.3

      \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;x \cdot \left(y - a\right) \ne 0:\\ \;\;\;\;{\left(\frac{\frac{z}{x}}{y - a}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - a}{z} \cdot x\\ } \end{array}} + t \]

   7. Simplified 0.3

      \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\left(y - a\right) \cdot x \ne 0:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x}}{a - y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - a}{z} \cdot x\\ } \end{array}} + t \]
      Proof

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

   1. Initial program 7.4

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

   2. Simplified 7.3

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

   3. Applied egg-rr 3.9

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

   4. Simplified 3.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - t, \frac{y - z}{z - a}, x\right)} \]
      Proof
3. Recombined 3 regimes into one program.

Alternatives

Alternative 1
Error	5.5
Cost	3532

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-306}:\\ \;\;\;\;x + \frac{\left(x - t\right) \cdot \left(y - z\right)}{z - a}\\ \mathbf{elif}\;t_1 \leq 10^{-289}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;x \ne 0:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - a}{z} \cdot x\\ \end{array} + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	3.5
Cost	2892

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-306}:\\ \;\;\;\;x - \left(t - x\right) \cdot \left(\frac{1}{z - a} \cdot \left(y - z\right)\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;\left(y - a\right) \cdot x \ne 0:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x}}{a - y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - a}{z} \cdot x\\ \end{array} + t\\ \mathbf{else}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{y - z}{z - a}\\ \end{array} \]

Alternative 3
Error	3.5
Cost	2892

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-306}:\\ \;\;\;\;x - \begin{array}{l} \mathbf{if}\;z - y \ne 0:\\ \;\;\;\;\frac{t - x}{\frac{z - a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - y}{a - z} \cdot \left(t - x\right)\\ \end{array}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;\left(y - a\right) \cdot x \ne 0:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x}}{a - y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - a}{z} \cdot x\\ \end{array} + t\\ \mathbf{else}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{y - z}{z - a}\\ \end{array} \]

Alternative 4
Error	6.4
Cost	2632

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{-289}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;x \ne 0:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - a}{z} \cdot x\\ \end{array} + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	3.5
Cost	2632

\[\begin{array}{l} t_1 := x - \left(t - x\right) \cdot \frac{y - z}{z - a}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;x \ne 0:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - a}{z} \cdot x\\ \end{array} + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	3.5
Cost	2632

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-306}:\\ \;\;\;\;x - \left(t - x\right) \cdot \left(\frac{1}{z - a} \cdot \left(y - z\right)\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;x \ne 0:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - a}{z} \cdot x\\ \end{array} + t\\ \mathbf{else}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{y - z}{z - a}\\ \end{array} \]

Alternative 7
Error	23.2
Cost	1500

\[\begin{array}{l} t_1 := \frac{t - x}{z}\\ t_2 := \frac{y - a}{z} \cdot x + t\\ t_3 := \frac{y \cdot \left(t - x\right)}{a} + x\\ \mathbf{if}\;z \leq -1.82 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-34}:\\ \;\;\;\;x - \frac{t \cdot z}{a}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+26}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+109}:\\ \;\;\;\;t - t_1 \cdot y\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+125}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+179}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot a + t\\ \end{array} \]

Alternative 8
Error	23.0
Cost	1368

\[\begin{array}{l} t_1 := \frac{y - a}{z} \cdot x + t\\ t_2 := \frac{y \cdot \left(t - x\right)}{a} + x\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.1 \cdot 10^{-34}:\\ \;\;\;\;x - \frac{t \cdot z}{a}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 75000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+104}:\\ \;\;\;\;t \cdot \frac{z - \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+125}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	22.8
Cost	1368

\[\begin{array}{l} t_1 := \frac{t - x}{z}\\ t_2 := \frac{y - a}{z} \cdot x + t\\ t_3 := \frac{y \cdot \left(t - x\right)}{a} + x\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-108}:\\ \;\;\;\;x - \frac{\left(z - y\right) \cdot t}{a}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+25}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+109}:\\ \;\;\;\;t - t_1 \cdot y\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+125}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+179}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot a + t\\ \end{array} \]

Alternative 10
Error	20.2
Cost	1368

\[\begin{array}{l} t_1 := x - \left(t - x\right) \cdot \frac{y}{-a}\\ t_2 := \frac{t - x}{z}\\ t_3 := t - t_2 \cdot y\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+33}:\\ \;\;\;\;\frac{y - a}{z} \cdot x + t\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+109}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+150}:\\ \;\;\;\;\frac{\left(y - a\right) \cdot x}{z} + t\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+218}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot a + t\\ \end{array} \]

Alternative 11
Error	34.6
Cost	1240

\[\begin{array}{l} t_1 := x - \frac{t \cdot z}{a}\\ t_2 := \frac{y}{a} \cdot \left(t - x\right)\\ t_3 := t - \frac{x \cdot a}{z}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+29}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-240}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-151}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-83}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 12
Error	29.3
Cost	1236

\[\begin{array}{l} t_1 := x - \frac{-t \cdot y}{a}\\ t_2 := t \cdot \frac{z - \left(y - a\right)}{z}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 15500000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+178}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	19.8
Cost	1232

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -2 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1300000:\\ \;\;\;\;\frac{y - a}{z} \cdot x + t\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+41}:\\ \;\;\;\;\frac{\left(t - x\right) \cdot \left(a - y\right)}{z} + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	19.4
Cost	1232

\[\begin{array}{l} t_1 := x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{if}\;a \leq -3 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -760000:\\ \;\;\;\;\frac{y - a}{z} \cdot x + t\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-30}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{+38}:\\ \;\;\;\;\frac{\left(t - x\right) \cdot \left(a - y\right)}{z} + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	19.4
Cost	1232

\[\begin{array}{l} t_1 := x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -95000:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;x \ne 0:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - a}{z} \cdot x\\ \end{array} + t\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-31}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+39}:\\ \;\;\;\;\frac{\left(t - x\right) \cdot \left(a - y\right)}{z} + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	28.7
Cost	1104

\[\begin{array}{l} t_1 := x - \frac{-t \cdot y}{a}\\ t_2 := \frac{t - x}{z} \cdot a + t\\ \mathbf{if}\;z \leq -2.95 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1850000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+101}:\\ \;\;\;\;t \cdot \frac{z - \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Error	25.0
Cost	1104

\[\begin{array}{l} t_1 := x - \frac{-t \cdot y}{a}\\ t_2 := \frac{y - a}{z} \cdot x + t\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 38000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+109}:\\ \;\;\;\;t \cdot \frac{z - \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Error	35.0
Cost	976

\[\begin{array}{l} t_1 := t - \frac{x \cdot a}{z}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-153}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-83}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	19.1
Cost	968

\[\begin{array}{l} t_1 := \frac{y - a}{z} \cdot x + t\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+125}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 20
Error	36.3
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -1.1:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-152}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-83}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 21
Error	30.1
Cost	776

\[\begin{array}{l} t_1 := t - \frac{x \cdot a}{z}\\ \mathbf{if}\;z \leq -1.28 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+126}:\\ \;\;\;\;x - \frac{-t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 22
Error	35.9
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -16:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 23
Error	45.8
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023033 
(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)))))