Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 14.8 → 3.7

Time: 46.8s

Precision: binary64

Cost: 8904

Math

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

↓

\[\begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 (fma (- t x) (/ (- y z) (- a z)) x))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -2e-293)
     t_1
     (if (<= t_2 0.0) (- t (* (/ (- t x) z) (- y a))) t_1))))

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 = fma((t - x), ((y - z) / (a - z)), x);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -2e-293) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t - (((t - x) / z) * (y - a));
	} else {
		tmp = t_1;
	}
	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 = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -2e-293)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)));
	else
		tmp = t_1;
	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[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-293], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 7.5

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

   2. Simplified 4.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
      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)): 2 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): 103 points increase in error, 13 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): 27 points increase in error, 100 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 61.5

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

   2. Applied egg-rr 61.5

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

   3. Taylor expanded in z around inf 11.1

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

   4. Simplified 0.9

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]
      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))))): 24 points increase in error, 29 points decrease in error
      (-.f64 t (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 t x) (-.f64 y a)) z))): 51 points increase in error, 22 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, 0 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))))): 2 points increase in error, 1 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
3. Recombined 2 regimes into one program.

4. Final simplification 3.7

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

Alternatives

Alternative 1
Error	7.2
Cost	2632

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{-210}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	24.4
Cost	1500

\[\begin{array}{l} t_1 := x - t \cdot \frac{z}{a}\\ t_2 := t + \frac{y - a}{\frac{z}{x}}\\ \mathbf{if}\;z \leq -2.9426793673236367 \cdot 10^{+109}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -484489518.32149315:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.1261910771288048:\\ \;\;\;\;t + \frac{t}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;z \leq -5.149600259341313 \cdot 10^{-22}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-94}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.738369557299789 \cdot 10^{+19}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq 1.4805273746873535 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	21.3
Cost	1368

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y}}\\ t_2 := t + \frac{y - a}{\frac{z}{x}}\\ \mathbf{if}\;z \leq -1.88177966163057 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-289}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.738369557299789 \cdot 10^{+19}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.4805273746873535 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	34.6
Cost	1240

\[\begin{array}{l} t_1 := t + \frac{x \cdot y}{z}\\ \mathbf{if}\;z \leq -1.88177966163057 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq -1.07 \cdot 10^{-134}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-170}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3461495599211315 \cdot 10^{+138}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	23.7
Cost	1236

\[\begin{array}{l} t_1 := t + \frac{y - a}{\frac{z}{x}}\\ \mathbf{if}\;z \leq -2.9426793673236367 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -484489518.32149315:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq -0.1261910771288048:\\ \;\;\;\;t + \frac{t}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;z \leq -5.149600259341313 \cdot 10^{-22}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.4805273746873535 \cdot 10^{+87}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	20.9
Cost	1236

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y}}\\ t_2 := t + \frac{y - a}{\frac{z}{x}}\\ \mathbf{if}\;z \leq -1.88177966163057 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-110}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.738369557299789 \cdot 10^{+19}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.4805273746873535 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	15.6
Cost	1232

\[\begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t}}\\ t_2 := t + \frac{y - a}{\frac{z}{x}}\\ \mathbf{if}\;z \leq -1.2023703340738331 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-289}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.085151857107415 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	15.2
Cost	1232

\[\begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{if}\;z \leq -1.2023703340738331 \cdot 10^{+119}:\\ \;\;\;\;t + \frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-289}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.085151857107415 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \end{array} \]

Alternative 9
Error	14.4
Cost	1232

\[\begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t}}\\ t_2 := t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -1.2023703340738331 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-289}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.085151857107415 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	14.2
Cost	1232

\[\begin{array}{l} t_1 := x - t \cdot \frac{z - y}{a - z}\\ t_2 := t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -3.634705079014071 \cdot 10^{+135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-289}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.085151857107415 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	27.5
Cost	1108

\[\begin{array}{l} t_1 := t + \frac{x \cdot y}{z}\\ \mathbf{if}\;z \leq -2.9426793673236367 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -484489518.32149315:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq -0.1261910771288048:\\ \;\;\;\;t + \frac{t}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;z \leq -5.149600259341313 \cdot 10^{-22}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.4805273746873535 \cdot 10^{+87}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	23.9
Cost	1104

\[\begin{array}{l} t_1 := t + \frac{y - a}{\frac{z}{x}}\\ \mathbf{if}\;z \leq -1.88177966163057 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-109}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.738369557299789 \cdot 10^{+19}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.4805273746873535 \cdot 10^{+87}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	22.6
Cost	1104

\[\begin{array}{l} t_1 := x + t \cdot \frac{y - z}{a}\\ t_2 := t + \frac{y - a}{\frac{z}{x}}\\ \mathbf{if}\;z \leq -2.9426793673236367 \cdot 10^{+109}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.738369557299789 \cdot 10^{+19}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.4805273746873535 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Error	21.9
Cost	1104

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y}}\\ t_2 := t + \frac{y - a}{\frac{z}{x}}\\ \mathbf{if}\;z \leq -1.88177966163057 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.738369557299789 \cdot 10^{+19}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.4805273746873535 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	19.7
Cost	1104

\[\begin{array}{l} t_1 := t + \frac{y - a}{\frac{z}{x}}\\ \mathbf{if}\;z \leq -1.88177966163057 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-139}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-141}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.085151857107415 \cdot 10^{+141}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	9.5
Cost	1096

\[\begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -1.2467783538137027 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.085151857107415 \cdot 10^{+141}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	36.4
Cost	984

\[\begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -1.88177966163057 \cdot 10^{+61}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.07 \cdot 10^{-134}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -3.485 \cdot 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3461495599211315 \cdot 10^{+138}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18
Error	36.4
Cost	984

\[\begin{array}{l} \mathbf{if}\;z \leq -1.88177966163057 \cdot 10^{+61}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-112}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -1.07 \cdot 10^{-134}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-170}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3461495599211315 \cdot 10^{+138}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19
Error	36.5
Cost	984

\[\begin{array}{l} \mathbf{if}\;z \leq -1.88177966163057 \cdot 10^{+61}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq -1.07 \cdot 10^{-134}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-170}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3461495599211315 \cdot 10^{+138}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20
Error	36.5
Cost	852

\[\begin{array}{l} \mathbf{if}\;z \leq -0.003637529066001391:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-106}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-170}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3461495599211315 \cdot 10^{+138}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 21
Error	36.2
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -0.003637529066001391:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-105}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3461495599211315 \cdot 10^{+138}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 22
Error	27.0
Cost	712

\[\begin{array}{l} t_1 := t + \frac{x \cdot y}{z}\\ \mathbf{if}\;z \leq -1.88177966163057 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4805273746873535 \cdot 10^{+87}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 23
Error	35.3
Cost	588

\[\begin{array}{l} \mathbf{if}\;z \leq -1.88177966163057 \cdot 10^{+61}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3461495599211315 \cdot 10^{+138}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 24
Error	35.9
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -1.88177966163057 \cdot 10^{+61}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.4805273746873535 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 25
Error	45.8
Cost	64

\[t \]

Reproduce

herbie shell --seed 2022317 
(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)))))