Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 14.8 → 6.5

Time: 26.0s

Precision: binary64

Cost: 8004

Math

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

↓

\[\begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-303}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - z}{t - x}}{y - z}}\\ \end{array} \]

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 (* (- z y) (/ (- x t) (- a z))))))
   (if (<= t_1 -5e-303)
     (fma (- y z) (/ (- t x) (- a z)) x)
     (if (<= t_1 0.0)
       (+ t (* (/ x z) (- y a)))
       (+ x (/ 1.0 (/ (/ (- a z) (- t x)) (- y 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 + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if (t_1 <= -5e-303) {
		tmp = fma((y - z), ((t - x) / (a - z)), x);
	} else if (t_1 <= 0.0) {
		tmp = t + ((x / z) * (y - a));
	} else {
		tmp = x + (1.0 / (((a - z) / (t - x)) / (y - 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(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -5e-303)
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(x / z) * Float64(y - a)));
	else
		tmp = Float64(x + Float64(1.0 / Float64(Float64(Float64(a - z) / Float64(t - x)) / Float64(y - 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[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-303], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(x / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $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)))) < -4.9999999999999998e-303

   1. Initial program 7.4

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

   2. Simplified 7.4

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

      [Start] 7.4	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      +-commutative [=>] 7.4	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]
      fma-def [=>] 7.4	\[ \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

   if -4.9999999999999998e-303 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 61.6

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

   2. Simplified 61.3

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

      [Start] 61.6	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      +-commutative [=>] 61.6	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]
      fma-def [=>] 61.3	\[ \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

   3. Taylor expanded in z around -inf 12.2

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

   4. Simplified 12.2

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

      [Start] 12.2	\[ -1 \cdot \frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z} + t \]
      +-commutative [=>] 12.2	\[ \color{blue}{t + -1 \cdot \frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z}} \]
      mul-1-neg [=>] 12.2	\[ t + \color{blue}{\left(-\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 12.2	\[ \color{blue}{t - \frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z}} \]
      +-commutative [=>] 12.2	\[ t - \frac{\color{blue}{y \cdot \left(t - x\right) + -1 \cdot \left(a \cdot \left(t - x\right)\right)}}{z} \]
      associate-*r* [=>] 12.2	\[ t - \frac{y \cdot \left(t - x\right) + \color{blue}{\left(-1 \cdot a\right) \cdot \left(t - x\right)}}{z} \]
      distribute-rgt-out [=>] 12.2	\[ t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y + -1 \cdot a\right)}}{z} \]
      mul-1-neg [=>] 12.2	\[ t - \frac{\left(t - x\right) \cdot \left(y + \color{blue}{\left(-a\right)}\right)}{z} \]

   5. Taylor expanded in t around 0 12.3

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

   6. Simplified 0.6

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

      [Start] 12.3	\[ t - -1 \cdot \frac{\left(y - a\right) \cdot x}{z} \]
      mul-1-neg [=>] 12.3	\[ t - \color{blue}{\left(-\frac{\left(y - a\right) \cdot x}{z}\right)} \]
      *-commutative [=>] 12.3	\[ t - \left(-\frac{\color{blue}{x \cdot \left(y - a\right)}}{z}\right) \]
      sub-neg [=>] 12.3	\[ t - \left(-\frac{x \cdot \color{blue}{\left(y + \left(-a\right)\right)}}{z}\right) \]
      associate-*l/ [<=] 0.6	\[ t - \left(-\color{blue}{\frac{x}{z} \cdot \left(y + \left(-a\right)\right)}\right) \]
      distribute-rgt-neg-in [=>] 0.6	\[ t - \color{blue}{\frac{x}{z} \cdot \left(-\left(y + \left(-a\right)\right)\right)} \]
      distribute-neg-in [=>] 0.6	\[ t - \frac{x}{z} \cdot \color{blue}{\left(\left(-y\right) + \left(-\left(-a\right)\right)\right)} \]
      +-commutative [=>] 0.6	\[ t - \frac{x}{z} \cdot \color{blue}{\left(\left(-\left(-a\right)\right) + \left(-y\right)\right)} \]
      remove-double-neg [=>] 0.6	\[ t - \frac{x}{z} \cdot \left(\color{blue}{a} + \left(-y\right)\right) \]
      sub-neg [<=] 0.6	\[ t - \frac{x}{z} \cdot \color{blue}{\left(a - y\right)} \]

   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. Applied egg-rr 18.7

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

   3. Applied egg-rr 17.8

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

   4. Applied egg-rr 18.7

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

   5. Simplified 7.4

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{a - z}{t - x}}{y - z}}} \]
      Proof

      [Start] 18.7	\[ x + \frac{1}{\frac{a - z}{\left(t - x\right) \cdot \left(y - z\right)}} \]
      associate-/r* [=>] 7.4	\[ x + \frac{1}{\color{blue}{\frac{\frac{a - z}{t - x}}{y - z}}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 6.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -5 \cdot 10^{-303}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - z}{t - x}}{y - z}}\\ \end{array} \]

Alternatives

Alternative 1
Error	6.5
Cost	2760

\[\begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - z}{t - x}}{y - z}}\\ \end{array} \]

Alternative 2
Error	6.4
Cost	2633

\[\begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-303} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \end{array} \]

Alternative 3
Error	19.7
Cost	1496

\[\begin{array}{l} t_1 := x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+85}:\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3600000:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-191}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+90}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	17.9
Cost	1496

\[\begin{array}{l} t_1 := x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+85}:\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4500000:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-190}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+92}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	17.9
Cost	1496

\[\begin{array}{l} t_1 := x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+85}:\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -80000:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-189}:\\ \;\;\;\;\frac{1}{\frac{\frac{a - z}{y - z}}{t}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+91}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	28.6
Cost	1372

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := t + y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-194}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-221}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-161}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+70}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	23.8
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := t + y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-109}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+69}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+185}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	22.8
Cost	1236

\[\begin{array}{l} t_1 := x - \frac{z - y}{\frac{a}{t}}\\ t_2 := t + y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -3.05 \cdot 10^{+43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-102}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-52}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	20.2
Cost	1236

\[\begin{array}{l} t_1 := x - \frac{z - y}{\frac{a}{t}}\\ t_2 := t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-53}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	20.3
Cost	1236

\[\begin{array}{l} t_1 := x - \frac{z - y}{\frac{a}{t}}\\ t_2 := t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{t - x}}{y}}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-50}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	23.5
Cost	1104

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + y \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-173}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	22.3
Cost	1104

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-177}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	20.9
Cost	1104

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-45}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Error	33.6
Cost	976

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+58}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15
Error	33.5
Cost	976

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+52}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t}{\frac{z}{a}}\\ \end{array} \]

Alternative 16
Error	36.1
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+41}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-221}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-147}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17
Error	36.1
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+41}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-221}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18
Error	27.8
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+42} \lor \neg \left(z \leq 3.1 \cdot 10^{+69}\right):\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 19
Error	25.5
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+41} \lor \neg \left(z \leq 3.1 \cdot 10^{+69}\right):\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 20
Error	29.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+41}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+70}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t}{\frac{z}{a}}\\ \end{array} \]

Alternative 21
Error	29.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+70}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t}{\frac{z}{a}}\\ \end{array} \]

Alternative 22
Error	35.5
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+41}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 23
Error	45.7
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023031 
(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)))))