Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 14.5 → 4.9

Time: 30.4s

Precision: binary64

Cost: 8004

Math

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

↓

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-293}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]

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-293)
     (fma (- t x) (/ (- y z) (- a z)) x)
     (if (<= t_1 0.0)
       (+ t (* (/ x z) (- y a)))
       (+ x (/ (- y z) (/ (- a z) (- t 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;
	if (t_1 <= -2e-293) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else if (t_1 <= 0.0) {
		tmp = t + ((x / z) * (y - a));
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - 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(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -2e-293)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(x / z) * Float64(y - a)));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - 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[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-293], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $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[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $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)))) < -2.0000000000000001e-293

   1. Initial program 7.3

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

   2. Simplified 3.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
      Proof
      (fma.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z)) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z))) x)): 0 points increase in error, 1 points decrease in error
      (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (-.f64 t x) (-.f64 y z)) (-.f64 a z))) x): 94 points increase in error, 23 points decrease in error
      (+.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 y z) (-.f64 t x))) (-.f64 a z)) x): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) x): 36 points increase in error, 97 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))): 0 points increase in error, 0 points decrease in error

   if -2.0000000000000001e-293 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 60.7

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

   2. Taylor expanded in z around inf 11.4

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

   3. Simplified 1.5

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]
      Proof
      (-.f64 t (*.f64 (/.f64 (-.f64 t x) z) (-.f64 y a))): 0 points increase in error, 0 points decrease in error
      (-.f64 t (Rewrite<= associate-/r/_binary64 (/.f64 (-.f64 t x) (/.f64 z (-.f64 y a))))): 33 points increase in error, 22 points decrease in error
      (-.f64 t (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 t x) (-.f64 y a)) z))): 43 points increase in error, 21 points decrease in error
      (-.f64 t (/.f64 (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 y (-.f64 t x)) (*.f64 a (-.f64 t x)))) z)): 2 points increase in error, 2 points decrease in error
      (Rewrite<= unsub-neg_binary64 (+.f64 t (neg.f64 (/.f64 (-.f64 (*.f64 y (-.f64 t x)) (*.f64 a (-.f64 t x))) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (-.f64 (*.f64 y (-.f64 t x)) (*.f64 a (-.f64 t x))) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (*.f64 -1 (Rewrite=> div-sub_binary64 (-.f64 (/.f64 (*.f64 y (-.f64 t x)) z) (/.f64 (*.f64 a (-.f64 t x)) z))))): 0 points increase in error, 3 points decrease in error
      (+.f64 t (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 -1 (/.f64 (*.f64 y (-.f64 t x)) z)) (*.f64 -1 (/.f64 (*.f64 a (-.f64 t x)) z))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 t (*.f64 -1 (/.f64 (*.f64 y (-.f64 t x)) z))) (*.f64 -1 (/.f64 (*.f64 a (-.f64 t x)) z)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (*.f64 y (-.f64 t x)) z)) t)) (*.f64 -1 (/.f64 (*.f64 a (-.f64 t x)) z))): 0 points increase in error, 0 points decrease in error

   4. Applied egg-rr 2.8

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

   5. Taylor expanded in t around 0 11.4

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

   6. Simplified 1.5

      \[\leadsto t - \color{blue}{\frac{x}{z} \cdot \left(a - y\right)} \]
      Proof
      (*.f64 (/.f64 x z) (-.f64 a y)): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 x z) (Rewrite<= unsub-neg_binary64 (+.f64 a (neg.f64 y)))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 x z) (+.f64 a (Rewrite=> neg-mul-1_binary64 (*.f64 -1 y)))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 x z) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 y) a))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 x z) (+.f64 (Rewrite<= neg-mul-1_binary64 (neg.f64 y)) a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 x z) (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 y)) a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 x z) (Rewrite<= associate--r-_binary64 (-.f64 0 (-.f64 y a)))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 x z) (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 y a)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (/.f64 x z) (-.f64 y a)))): 0 points increase in error, 0 points decrease in error
      (neg.f64 (Rewrite<= associate-/r/_binary64 (/.f64 x (/.f64 z (-.f64 y a))))): 51 points increase in error, 55 points decrease in error
      (neg.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 x (-.f64 y a)) z))): 44 points increase in error, 40 points decrease in error
      (neg.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 y a) x)) z)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (*.f64 (-.f64 y a) x) z))): 0 points increase in error, 0 points decrease in error

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

   1. Initial program 6.9

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

   2. Applied egg-rr 6.9

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 4.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-293}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]

Alternatives

Alternative 1
Error	6.5
Cost	2632

\[\begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t - x}}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	29.0
Cost	1632

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := t - y \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -2.464685605591098 \cdot 10^{-9}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.922413527563469 \cdot 10^{-22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.067111666255744 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 9.54368543782231 \cdot 10^{+97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.112321781543354 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;z \leq 2.8144138130423207 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.301370831752978 \cdot 10^{+165}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \end{array} \]

Alternative 3
Error	36.0
Cost	1372

\[\begin{array}{l} t_1 := t - y \cdot \frac{t}{z}\\ t_2 := \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -2.117313148752723 \cdot 10^{+222}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.0196617850079683 \cdot 10^{+152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.7329719587879198 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.6302738915696925 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.517497591382997 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.0337248611707329 \cdot 10^{+249}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	30.8
Cost	1372

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := t - y \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -2.464685605591098 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.922413527563469 \cdot 10^{-22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.067111666255744 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 1.778074702029574 \cdot 10^{+100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.112321781543354 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.8144138130423207 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	30.8
Cost	1372

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := t - y \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -2.464685605591098 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.922413527563469 \cdot 10^{-22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.067111666255744 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 9.54368543782231 \cdot 10^{+97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.112321781543354 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;z \leq 2.8144138130423207 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	28.4
Cost	1372

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := t + x \cdot \frac{y}{z}\\ t_3 := t - y \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -2.464685605591098 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.922413527563469 \cdot 10^{-22}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.067111666255744 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 9.54368543782231 \cdot 10^{+97}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6.112321781543354 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;z \leq 2.8144138130423207 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	20.2
Cost	1232

\[\begin{array}{l} t_1 := t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -1.1572860338805904 \cdot 10^{+204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.9769563607490076 \cdot 10^{+79}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq -2.464685605591098 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-115}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	20.3
Cost	1232

\[\begin{array}{l} t_1 := t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -1.1572860338805904 \cdot 10^{+204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.9769563607490076 \cdot 10^{+79}:\\ \;\;\;\;x - \frac{z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq -2.464685605591098 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-115}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	20.6
Cost	1232

\[\begin{array}{l} t_1 := t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -1.1572860338805904 \cdot 10^{+204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.9769563607490076 \cdot 10^{+79}:\\ \;\;\;\;x - \frac{z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq -2.464685605591098 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-115}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \left(y - a\right) \cdot \frac{t - x}{z}\\ \end{array} \]

Alternative 10
Error	24.6
Cost	1104

\[\begin{array}{l} t_1 := t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -1.1572860338805904 \cdot 10^{+204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.9769563607490076 \cdot 10^{+79}:\\ \;\;\;\;\frac{t}{\frac{a - z}{-z}}\\ \mathbf{elif}\;z \leq -2.464685605591098 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-107}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	21.1
Cost	1104

\[\begin{array}{l} \mathbf{if}\;z \leq -2.464685605591098 \cdot 10^{-9}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq 10^{-105}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3202901.88105065:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{elif}\;z \leq 5.097136767534751 \cdot 10^{+57}:\\ \;\;\;\;x - \frac{z \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y}{z}\\ \end{array} \]

Alternative 12
Error	22.0
Cost	1104

\[\begin{array}{l} \mathbf{if}\;z \leq -1.1572860338805904 \cdot 10^{+204}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq -8.850870672210957 \cdot 10^{+53}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq -2.464685605591098 \cdot 10^{-9}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;z \leq 10^{-100}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y}{z}\\ \end{array} \]

Alternative 13
Error	34.7
Cost	976

\[\begin{array}{l} t_1 := t - y \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -1.6350902775357252 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3369895863731887 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.2075215800084104 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	35.1
Cost	976

\[\begin{array}{l} t_1 := t - y \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -1.6350902775357252 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.922413527563469 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.2075215800084104 \cdot 10^{+79}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	23.4
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -2.464685605591098 \cdot 10^{-9}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-103}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y}{z}\\ \end{array} \]

Alternative 16
Error	20.8
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -2.464685605591098 \cdot 10^{-9}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;z \leq 10^{-105}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y}{z}\\ \end{array} \]

Alternative 17
Error	20.8
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -2.464685605591098 \cdot 10^{-9}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq 10^{-105}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y}{z}\\ \end{array} \]

Alternative 18
Error	21.5
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -2.464685605591098 \cdot 10^{-9}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq 10^{-100}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y}{z}\\ \end{array} \]

Alternative 19
Error	35.8
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -6.018350377078143 \cdot 10^{-27}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.2075215800084104 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20
Error	45.9
Cost	64

\[t \]

Reproduce

herbie shell --seed 2022294 
(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)))))