Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 14.3 → 7.0

Time: 32.8s

Precision: binary64

Cost: 8904

Math

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

↓

\[\begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]

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) (/ (- x t) (- a z))))))
   (if (<= t_1 -2e-147)
     t_1
     (if (<= t_1 0.0)
       (+ t (* (- y a) (/ x z)))
       (fma (- y z) (/ (- t x) (- a z)) 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) * ((x - t) / (a - z)));
	double tmp;
	if (t_1 <= -2e-147) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + ((y - a) * (x / z));
	} else {
		tmp = fma((y - z), ((t - x) / (a - z)), 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(x - t) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -2e-147)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(x / z)));
	else
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), 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[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-147], t$95$1, If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $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)))) < -1.9999999999999999e-147

   1. Initial program 4.9

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

   if -1.9999999999999999e-147 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 52.4

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

   2. Simplified 52.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]
      Proof
      (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))) x)): 0 points increase in error, 3 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

   3. Taylor expanded in z around -inf 18.5

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

   4. Simplified 11.5

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y + \left(-a\right)}}} \]
      Proof
      (-.f64 t (/.f64 (-.f64 t x) (/.f64 z (+.f64 y (neg.f64 a))))): 0 points increase in error, 0 points decrease in error
      (-.f64 t (/.f64 (-.f64 t x) (/.f64 z (+.f64 y (Rewrite<= mul-1-neg_binary64 (*.f64 -1 a)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 t (/.f64 (-.f64 t x) (/.f64 z (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 a) y))))): 9 points increase in error, 0 points decrease in error
      (-.f64 t (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 t x) (+.f64 (*.f64 -1 a) y)) z))): 0 points increase in error, 3 points decrease in error
      (-.f64 t (/.f64 (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 (*.f64 -1 a) (-.f64 t x)) (*.f64 y (-.f64 t x)))) z)): 3 points increase in error, 0 points decrease in error
      (-.f64 t (/.f64 (+.f64 (Rewrite<= associate-*r*_binary64 (*.f64 -1 (*.f64 a (-.f64 t x)))) (*.f64 y (-.f64 t x))) z)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= unsub-neg_binary64 (+.f64 t (neg.f64 (/.f64 (+.f64 (*.f64 -1 (*.f64 a (-.f64 t x))) (*.f64 y (-.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 -1 (*.f64 a (-.f64 t x))) (*.f64 y (-.f64 t x))) z)))): 0 points increase in error, 9 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -1 (*.f64 a (-.f64 t x))) (*.f64 y (-.f64 t x))) z)) t)): 9 points increase in error, 0 points decrease in error

   5. Taylor expanded in z around 0 18.5

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

   6. Simplified 11.0

      \[\leadsto t - \color{blue}{\left(y - a\right) \cdot \frac{t - x}{z}} \]
      Proof
      (-.f64 t (*.f64 (-.f64 y a) (/.f64 (-.f64 t x) z))): 0 points increase in error, 0 points decrease in error
      (-.f64 t (*.f64 (Rewrite=> sub-neg_binary64 (+.f64 y (neg.f64 a))) (/.f64 (-.f64 t x) z))): 0 points increase in error, 0 points decrease in error
      (-.f64 t (*.f64 (Rewrite=> +-commutative_binary64 (+.f64 (neg.f64 a) y)) (/.f64 (-.f64 t x) z))): 12 points increase in error, 0 points decrease in error
      (-.f64 t (*.f64 (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 a)) y) (/.f64 (-.f64 t x) z))): 0 points increase in error, 6 points decrease in error
      (-.f64 t (*.f64 (Rewrite<= associate--r-_binary64 (-.f64 0 (-.f64 a y))) (/.f64 (-.f64 t x) z))): 6 points increase in error, 0 points decrease in error
      (-.f64 t (*.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 a y))) (/.f64 (-.f64 t x) z))): 0 points increase in error, 0 points decrease in error
      (-.f64 t (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (neg.f64 (-.f64 a y)) (-.f64 t x)) z))): 0 points increase in error, 0 points decrease in error
      (-.f64 t (/.f64 (*.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (-.f64 a y))) (-.f64 t x)) z)): 0 points increase in error, 12 points decrease in error
      (-.f64 t (/.f64 (*.f64 (Rewrite=> associate--r-_binary64 (+.f64 (-.f64 0 a) y)) (-.f64 t x)) z)): 12 points increase in error, 0 points decrease in error
      (-.f64 t (/.f64 (*.f64 (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 a)) y) (-.f64 t x)) z)): 0 points increase in error, 6 points decrease in error
      (-.f64 t (/.f64 (*.f64 (Rewrite<= +-commutative_binary64 (+.f64 y (neg.f64 a))) (-.f64 t x)) z)): 6 points increase in error, 0 points decrease in error
      (-.f64 t (/.f64 (*.f64 (Rewrite<= sub-neg_binary64 (-.f64 y a)) (-.f64 t x)) z)): 0 points increase in error, 0 points decrease in error

   7. Taylor expanded in t around 0 19.0

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

   8. Simplified 11.0

      \[\leadsto t - \color{blue}{\left(y - a\right) \cdot \frac{-x}{z}} \]
      Proof
      (-.f64 t (*.f64 (-.f64 y a) (/.f64 (neg.f64 x) z))): 0 points increase in error, 0 points decrease in error
      (-.f64 t (*.f64 (-.f64 y a) (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 x z))))): 0 points increase in error, 0 points decrease in error
      (-.f64 t (Rewrite=> distribute-rgt-neg-out_binary64 (neg.f64 (*.f64 (-.f64 y a) (/.f64 x z))))): 5 points increase in error, 0 points decrease in error
      (-.f64 t (neg.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (-.f64 y a) x) z)))): 0 points increase in error, 3 points decrease in error
      (-.f64 t (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (*.f64 (-.f64 y a) x) z)))): 3 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 7.4

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

   2. Simplified 7.3

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]
      Proof
      (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))) x)): 0 points increase in error, 3 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
3. Recombined 3 regimes into one program.

4. Final simplification 7.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq -2 \cdot 10^{-147}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq 0:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	7.0
Cost	2633

\[\begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-147} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \]

Alternative 2
Error	43.3
Cost	2036

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ t_2 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;x \leq -1.16 \cdot 10^{+145}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+82}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-88}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq -1.28 \cdot 10^{-169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-265}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-214}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+40}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+162}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+219}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+235}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	43.5
Cost	2036

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;x \leq -1.22 \cdot 10^{+145}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{+76}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-91}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-222}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-265}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-214}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-191}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 6.7 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+40}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+164}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+219}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+235}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	42.6
Cost	1504

\[\begin{array}{l} t_1 := y \cdot \frac{x - t}{z}\\ \mathbf{if}\;y \leq -8.8 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{+61}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-162}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+108}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 5
Error	28.4
Cost	1373

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{y}{\frac{-a}{x}}\\ \mathbf{if}\;x \leq -1.22 \cdot 10^{+145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{+243} \lor \neg \left(x \leq 6.8 \cdot 10^{+282}\right):\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	22.9
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := t + x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+170}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-54}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.38 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+73}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	22.9
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := t + x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+168}:\\ \;\;\;\;t + \frac{a}{-\frac{z}{x}}\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.38 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+75}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	20.7
Cost	1236

\[\begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -8.6 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-10}:\\ \;\;\;\;t + \frac{a}{-\frac{z}{x}}\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-59}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-40}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+104}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	20.6
Cost	1236

\[\begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-9}:\\ \;\;\;\;t + \frac{a}{-\frac{z}{x}}\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-40}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+104}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	20.6
Cost	1236

\[\begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-10}:\\ \;\;\;\;t + \frac{a}{-\frac{z}{x}}\\ \mathbf{elif}\;a \leq -4.95 \cdot 10^{-60}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-40}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	18.2
Cost	1232

\[\begin{array}{l} t_1 := t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-54}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 4.38 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	18.0
Cost	1232

\[\begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+43}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-54}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 4.38 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 13
Error	26.8
Cost	1108

\[\begin{array}{l} t_1 := t + x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+170}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-39}:\\ \;\;\;\;\left(-x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-54}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	27.0
Cost	1108

\[\begin{array}{l} t_1 := t + x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -3.05 \cdot 10^{+168}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -72000:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-37}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a - z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-54}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	20.2
Cost	1104

\[\begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+48}:\\ \;\;\;\;t + \frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-54}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 62000000000000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 4.38 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \]

Alternative 16
Error	20.1
Cost	1104

\[\begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+44}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 10^{+15}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 4.38 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \]

Alternative 17
Error	29.3
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+92}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-40}:\\ \;\;\;\;\left(-x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \end{array} \]

Alternative 18
Error	37.5
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{+92}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-202}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-80}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19
Error	27.7
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+92} \lor \neg \left(z \leq 2.5 \cdot 10^{+23}\right):\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 20
Error	30.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+92}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 21
Error	28.7
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+92}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-54}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \end{array} \]

Alternative 22
Error	36.4
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+92}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 23
Error	45.6
Cost	64

\[t \]

Reproduce

herbie shell --seed 2022343 
(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)))))