Average Error: 14.7 → 3.6
Time: 49.5s
Precision: binary64
Cost: 8904
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
↓
\[\begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ t_2 := x + \frac{x - t}{a - z} \cdot \left(z - y\right)\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
(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 (* (/ (- x t) (- a z)) (- z y)))))
   (if (<= t_2 -5e-296)
     t_1
     (if (<= t_2 0.0) (+ t (* (/ (- t x) z) (- a y))) 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 + (((x - t) / (a - z)) * (z - y));
	double tmp;
	if (t_2 <= -5e-296) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) / z) * (a - y));
	} 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(Float64(x - t) / Float64(a - z)) * Float64(z - y)))
	tmp = 0.0
	if (t_2 <= -5e-296)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	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[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-296], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $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 + \frac{x - t}{a - z} \cdot \left(z - y\right)\\
\mathbf{if}\;t_2 \leq -5 \cdot 10^{-296}:\\
\;\;\;\;t_1\\

\mathbf{elif}\;t_2 \leq 0:\\
\;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\

\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)))) < -5.0000000000000003e-296 or 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. Simplified4.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
      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)): 3 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (-.f64 t x) (-.f64 y z)) (-.f64 a z))) x): 93 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): 40 points increase in error, 82 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 -5.0000000000000003e-296 < (+.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-rr61.4

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

    3. Taylor expanded in z around inf 10.8

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

    4. Simplified0.8

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]
      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))))): 28 points increase in error, 36 points decrease in error
      (-.f64 t (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 t x) (-.f64 y a)) z))): 51 points increase in error, 27 points decrease in error
      (-.f64 t (/.f64 (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 y (-.f64 t x)) (*.f64 a (-.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 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, 0 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 simplification3.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{x - t}{a - z} \cdot \left(z - y\right) \leq -5 \cdot 10^{-296}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;x + \frac{x - t}{a - z} \cdot \left(z - y\right) \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \]

Alternatives

Alternative 1
Error4.6
Cost4688
\[\begin{array}{l} t_1 := x + \frac{x - t}{a - z} \cdot \left(z - y\right)\\ t_2 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -20000:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-296}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x} - \frac{z}{t - x}}\\ \end{array} \]
Alternative 2
Error4.6
Cost4432
\[\begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t - x}}\\ t_2 := x + \frac{x - t}{a - z} \cdot \left(z - y\right)\\ t_3 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t_2 \leq -20000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-296}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-59}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 3
Error32.9
Cost2160
\[\begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ t_2 := x - \frac{z}{\frac{a - z}{t}}\\ t_3 := x - \frac{y}{a} \cdot \left(x - t\right)\\ t_4 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;x \leq -3.4129323979896316 \cdot 10^{+99}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -4.9975605004372723 \cdot 10^{-231}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.3462086890093315 \cdot 10^{-291}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 1.0565317002917754 \cdot 10^{-243}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.426408087428576 \cdot 10^{-156}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 9.88625160588926 \cdot 10^{-110}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;x \leq 2.0575291716951608 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.246436088989817 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.19932761666545 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.4321666852664944 \cdot 10^{+200}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+225}:\\ \;\;\;\;-x \cdot \frac{a}{z}\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+242}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \end{array} \]
Alternative 4
Error33.2
Cost1900
\[\begin{array}{l} t_1 := x - \frac{z}{\frac{a - z}{t}}\\ t_2 := x + \frac{y}{\frac{a}{t - x}}\\ t_3 := x - x \cdot \frac{y}{a}\\ t_4 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;x \leq -3.4129323979896316 \cdot 10^{+99}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -4.9975605004372723 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.3462086890093315 \cdot 10^{-291}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 1.0565317002917754 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.426408087428576 \cdot 10^{-156}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 9.88625160588926 \cdot 10^{-110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.0575291716951608 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.246436088989817 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 9.19932761666545 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.4321666852664944 \cdot 10^{+200}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+240}:\\ \;\;\;\;-x \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 5
Error33.2
Cost1900
\[\begin{array}{l} t_1 := x - \frac{z}{\frac{a - z}{t}}\\ t_2 := x + \frac{y}{\frac{a}{t - x}}\\ t_3 := x - x \cdot \frac{y}{a}\\ t_4 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;x \leq -3.4129323979896316 \cdot 10^{+99}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -4.9975605004372723 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.3462086890093315 \cdot 10^{-291}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 1.0565317002917754 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.426408087428576 \cdot 10^{-156}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 9.88625160588926 \cdot 10^{-110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.0575291716951608 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.246436088989817 \cdot 10^{-15}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 9.19932761666545 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.4321666852664944 \cdot 10^{+200}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+240}:\\ \;\;\;\;-x \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 6
Error33.2
Cost1900
\[\begin{array}{l} t_1 := x - \frac{z}{\frac{a - z}{t}}\\ t_2 := x - x \cdot \frac{y}{a}\\ t_3 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;x \leq -3.4129323979896316 \cdot 10^{+99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.9975605004372723 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.3462086890093315 \cdot 10^{-291}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.0565317002917754 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.426408087428576 \cdot 10^{-156}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 9.88625160588926 \cdot 10^{-110}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;x \leq 2.0575291716951608 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.246436088989817 \cdot 10^{-15}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 9.19932761666545 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.4321666852664944 \cdot 10^{+200}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+240}:\\ \;\;\;\;-x \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 7
Error30.7
Cost1764
\[\begin{array}{l} t_1 := x - \frac{z}{\frac{a - z}{t}}\\ t_2 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -2.8161887667693944 \cdot 10^{+173}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.924567852726917 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.781894099321528 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-61}:\\ \;\;\;\;\frac{t}{a - z} \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-165}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-287}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-115}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-65}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.0301372809371738 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 8
Error33.8
Cost1500
\[\begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;a \leq -7.781894099321528 \cdot 10^{+33}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-61}:\\ \;\;\;\;\frac{t}{a - z} \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-287}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-115}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-65}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.936715712075218 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t}}\\ \end{array} \]
Alternative 9
Error27.7
Cost1500
\[\begin{array}{l} t_1 := x - \frac{z}{\frac{a - z}{t}}\\ t_2 := x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -2.8161887667693944 \cdot 10^{+173}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.924567852726917 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.781894099321528 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 10^{-68}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 0.0011562739947521999:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 1.5196369639523276 \cdot 10^{+29}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;a \leq 6.777144533366083 \cdot 10^{+70}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 10
Error20.3
Cost1496
\[\begin{array}{l} t_1 := x - \frac{z}{\frac{a - z}{t}}\\ t_2 := x - \frac{y}{a} \cdot \left(x - t\right)\\ t_3 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;a \leq -2.8161887667693944 \cdot 10^{+173}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.924567852726917 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.964862385881313 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 10^{-66}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 0.0011562739947521999:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 6.777144533366083 \cdot 10^{+70}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 11
Error20.3
Cost1496
\[\begin{array}{l} t_1 := x - \frac{y}{a} \cdot \left(x - t\right)\\ t_2 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;a \leq -2.8161887667693944 \cdot 10^{+173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.924567852726917 \cdot 10^{+125}:\\ \;\;\;\;x + z \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;a \leq -5.964862385881313 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 10^{-66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 0.0011562739947521999:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 6.777144533366083 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a - z}{t}}\\ \end{array} \]
Alternative 12
Error20.3
Cost1496
\[\begin{array}{l} t_1 := x - \frac{y}{a} \cdot \left(x - t\right)\\ t_2 := t - \frac{a - y}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -2.8161887667693944 \cdot 10^{+173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.924567852726917 \cdot 10^{+125}:\\ \;\;\;\;x + z \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;a \leq -5.964862385881313 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 10^{-66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 0.0011562739947521999:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 6.777144533366083 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a - z}{t}}\\ \end{array} \]
Alternative 13
Error20.1
Cost1496
\[\begin{array}{l} t_1 := x - \frac{y}{a} \cdot \left(x - t\right)\\ t_2 := t - \frac{a - y}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -2.8161887667693944 \cdot 10^{+173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.924567852726917 \cdot 10^{+125}:\\ \;\;\;\;x + z \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;a \leq -5.964862385881313 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 10^{-66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 0.0011562739947521999:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 6.777144533366083 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a - z}{t - x}}\\ \end{array} \]
Alternative 14
Error27.2
Cost1236
\[\begin{array}{l} \mathbf{if}\;z \leq -2.622832124832092 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.110462361785214 \cdot 10^{+95}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -9.69112378243918 \cdot 10^{+51}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 10^{-10}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 4.2454715392228433 \cdot 10^{+183}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
Alternative 15
Error27.1
Cost1236
\[\begin{array}{l} \mathbf{if}\;z \leq -2.622832124832092 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.110462361785214 \cdot 10^{+95}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -9.69112378243918 \cdot 10^{+51}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-120}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 4.2454715392228433 \cdot 10^{+183}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
Alternative 16
Error15.1
Cost1232
\[\begin{array}{l} t_1 := x + t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -2.8228350788081454 \cdot 10^{+125}:\\ \;\;\;\;t - \frac{a - y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.05 \cdot 10^{-128}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 4.653495852066283 \cdot 10^{+199}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
Alternative 17
Error32.9
Cost1108
\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -2.622832124832092 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.110462361785214 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.69112378243918 \cdot 10^{+51}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 4.05 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.2454715392228433 \cdot 10^{+183}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
Alternative 18
Error31.2
Cost1108
\[\begin{array}{l} \mathbf{if}\;z \leq -2.622832124832092 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.110462361785214 \cdot 10^{+95}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -9.69112378243918 \cdot 10^{+51}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-111}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4.2454715392228433 \cdot 10^{+183}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
Alternative 19
Error31.1
Cost1108
\[\begin{array}{l} \mathbf{if}\;z \leq -2.622832124832092 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.110462361785214 \cdot 10^{+95}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -9.69112378243918 \cdot 10^{+51}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 4.05 \cdot 10^{-128}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.2454715392228433 \cdot 10^{+183}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
Alternative 20
Error10.2
Cost1096
\[\begin{array}{l} \mathbf{if}\;z \leq -1.9432187144868041 \cdot 10^{+208}:\\ \;\;\;\;t - \frac{a - y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 4.653495852066283 \cdot 10^{+199}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
Alternative 21
Error34.4
Cost976
\[\begin{array}{l} t_1 := x - \frac{z \cdot t}{a}\\ \mathbf{if}\;a \leq -5.964862385881313 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.887359300654938 \cdot 10^{+33}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 7.231985687697828 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 22
Error33.3
Cost976
\[\begin{array}{l} t_1 := x - \frac{z}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -5.964862385881313 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.887359300654938 \cdot 10^{+33}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 7.231985687697828 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 23
Error35.5
Cost592
\[\begin{array}{l} \mathbf{if}\;a \leq -5.964862385881313 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.887359300654938 \cdot 10^{+33}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 7.231985687697828 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 24
Error36.9
Cost328
\[\begin{array}{l} \mathbf{if}\;z \leq -1.300013867633317 \cdot 10^{+64}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.2454715392228433 \cdot 10^{+183}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
Alternative 25
Error46.1
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2022308 
(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)))))