Average Error: 14.9 → 3.6
Time: 38.5s
Precision: binary64
Cost: 8904
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
↓
\[\begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t - \frac{y - a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
(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 -1e-307)
     t_1
     (if (<= t_2 0.0) (- t (/ (- y a) (/ z (- t x)))) t_1))))
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 <= -1e-307) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t - ((y - a) / (z / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

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 <= -1e-307)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t - Float64(Float64(y - a) / Float64(z / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

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, -1e-307], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t - N[(N[(y - a), $MachinePrecision] / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

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 -1 \cdot 10^{-307}:\\
\;\;\;\;t_1\\

\mathbf{elif}\;t_2 \leq 0:\\
\;\;\;\;t - \frac{y - a}{\frac{z}{t - x}}\\

\mathbf{else}:\\
\;\;\;\;t_1\\


\end{array}

Error

Derivation

  1. Split input into 2 regimes

  2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.99999999999999909e-308 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. Simplified4.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
      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, 3 points decrease in error
      (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (-.f64 t x) (-.f64 y z)) (-.f64 a z))) x): 80 points increase in error, 16 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): 31 points increase in error, 84 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 -9.99999999999999909e-308 < (+.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. Simplified61.8

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
      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, 3 points decrease in error
      (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (-.f64 t x) (-.f64 y z)) (-.f64 a z))) x): 80 points increase in error, 16 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): 31 points increase in error, 84 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. Applied egg-rr61.8

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

    4. Taylor expanded in z around inf 10.0

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

    5. Simplified0.2

      \[\leadsto \color{blue}{t - \frac{y - a}{\frac{z}{t - x}}} \]
      Proof
      (-.f64 t (/.f64 (-.f64 y a) (/.f64 z (-.f64 t x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 t (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 y a) (-.f64 t x)) z))): 45 points increase in error, 29 points decrease in error
      (Rewrite<= unsub-neg_binary64 (+.f64 t (neg.f64 (/.f64 (*.f64 (-.f64 y a) (-.f64 t x)) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (Rewrite=> distribute-neg-frac_binary64 (/.f64 (neg.f64 (*.f64 (-.f64 y a) (-.f64 t x))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 t (/.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 (-.f64 y a) (-.f64 t x)))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 t (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 -1 (-.f64 y a)) (-.f64 t x))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 t (/.f64 (*.f64 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 -1 y) (*.f64 -1 a))) (-.f64 t x)) z)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (*.f64 (-.f64 (*.f64 -1 y) (*.f64 -1 a)) (-.f64 t x)) z) t)): 0 points increase in error, 0 points decrease in error
  3. Recombined 2 regimes into one program.

  4. Final simplification3.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-307}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t - \frac{y - a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \]

Alternatives

Alternative 1
Error6.2
Cost4432
\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-169}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+300}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]
Alternative 2
Error25.1
Cost2160
\[\begin{array}{l} t_1 := x - t \cdot \frac{z}{a}\\ t_2 := \frac{t}{\frac{a - z}{y - z}}\\ t_3 := x + x \cdot \frac{z - y}{a}\\ t_4 := t + x \cdot \frac{y - a}{z}\\ t_5 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -5.0175898428940687 \cdot 10^{+64}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -64283475.99384489:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.2052655384278461 \cdot 10^{-6}:\\ \;\;\;\;\frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq -1.2504252568196476 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-184}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-172}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-123}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8865079516370.02:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.3947400616510585 \cdot 10^{+38}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]
Alternative 3
Error28.8
Cost1632
\[\begin{array}{l} t_1 := \frac{t}{\frac{a - z}{y - z}}\\ t_2 := t + x \cdot \frac{y - a}{z}\\ t_3 := x + \frac{y \cdot \left(t - x\right)}{a}\\ t_4 := x + x \cdot \frac{z - y}{a}\\ \mathbf{if}\;x \leq -1 \cdot 10^{+260}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+198}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.585218268337018 \cdot 10^{-20}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{elif}\;x \leq 2.7118659776030605 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.590092202052017 \cdot 10^{-101}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 3.248662003097018 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 10^{+150}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 10^{+182}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]
Alternative 4
Error23.3
Cost1500
\[\begin{array}{l} t_1 := \frac{t}{\frac{a - z}{y - z}}\\ t_2 := x + \frac{y - z}{\frac{a}{t}}\\ t_3 := t + x \cdot \frac{y - a}{z}\\ \mathbf{if}\;a \leq -3.93793398358717 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-158}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-153}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-58}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 2.204758912297863 \cdot 10^{-16}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.2353027197531722 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 5
Error23.7
Cost1500
\[\begin{array}{l} t_1 := \frac{t}{\frac{a - z}{y - z}}\\ t_2 := t + x \cdot \frac{y - a}{z}\\ \mathbf{if}\;a \leq -3.93793398358717 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-153}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-58}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 2.204758912297863 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1539515385.335059:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
Alternative 6
Error18.9
Cost1232
\[\begin{array}{l} t_1 := t - \frac{y - a}{\frac{z}{t - x}}\\ \mathbf{if}\;z \leq -5.0175898428940687 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -64283475.99384489:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -1.2504252568196476 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.828448974858456 \cdot 10^{+60}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 7
Error17.2
Cost1232
\[\begin{array}{l} t_1 := t - \frac{y - a}{\frac{z}{t - x}}\\ \mathbf{if}\;z \leq -5.0175898428940687 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -64283475.99384489:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -1.2504252568196476 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.828448974858456 \cdot 10^{+60}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 8
Error15.2
Cost1232
\[\begin{array}{l} t_1 := x + y \cdot \frac{t - x}{a - z}\\ t_2 := t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -5.0175898428940687 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9.05385006153807 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.5961709488641545 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{1}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 1.6561132428681767 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 9
Error25.8
Cost1104
\[\begin{array}{l} t_1 := \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;a \leq -1.3555626972990665 \cdot 10^{+144}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.204758912297863 \cdot 10^{-16}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.7760391979173297 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
Alternative 10
Error21.9
Cost1104
\[\begin{array}{l} t_1 := \frac{t}{\frac{a - z}{y - z}}\\ t_2 := x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -3.93793398358717 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.204758912297863 \cdot 10^{-16}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.2353027197531722 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 11
Error16.3
Cost1100
\[\begin{array}{l} t_1 := t - \frac{y - a}{\frac{z}{t - x}}\\ \mathbf{if}\;z \leq -5.0175898428940687 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-125}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 4.828448974858456 \cdot 10^{+60}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 12
Error16.3
Cost1100
\[\begin{array}{l} t_1 := t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{if}\;z \leq -5.0175898428940687 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-125}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 4.828448974858456 \cdot 10^{+60}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 13
Error16.1
Cost1100
\[\begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -5.0175898428940687 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-125}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 4.467023421221431 \cdot 10^{+71}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 14
Error10.3
Cost1096
\[\begin{array}{l} \mathbf{if}\;z \leq -8.780538732637886 \cdot 10^{+144}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq 3.454658779449296 \cdot 10^{+175}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]
Alternative 15
Error31.1
Cost844
\[\begin{array}{l} t_1 := x - t \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -250230.2563631886:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.5724163050098182 \cdot 10^{+184}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 16
Error26.8
Cost840
\[\begin{array}{l} \mathbf{if}\;a \leq -1.3555626972990665 \cdot 10^{+144}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 1.7760391979173297 \cdot 10^{+35}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
Alternative 17
Error34.2
Cost712
\[\begin{array}{l} \mathbf{if}\;a \leq -4.2294738692101894 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
Alternative 18
Error30.1
Cost712
\[\begin{array}{l} \mathbf{if}\;a \leq -250230.2563631886:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 44.60023859731867:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
Alternative 19
Error36.7
Cost456
\[\begin{array}{l} \mathbf{if}\;a \leq -57479902.70451729:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-167}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
Alternative 20
Error35.8
Cost328
\[\begin{array}{l} \mathbf{if}\;a \leq -57479902.70451729:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.2353027197531722 \cdot 10^{+35}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 21
Error45.6
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2022291 
(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)))))