Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3

?

Percentage Accurate: 67.4% → 90.3%
Time: 25.2s
Precision: binary64
Cost: 8004

?

\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-266}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]
(FPCore (x y z t a) :precision binary64 (+ x (/ (* (- y x) (- z t)) (- a t))))
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 -1e-266)
     (fma (/ (- z t) (- a t)) (- y x) x)
     (if (<= t_1 0.0)
       (+ y (/ (- x y) (/ t (- z a))))
       (+ x (/ (- y x) (/ (- a t) (- z t))))))))
double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}
double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -1e-266) {
		tmp = fma(((z - t) / (a - t)), (y - x), x);
	} else if (t_1 <= 0.0) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	}
	return tmp;
}
function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
end
function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -1e-266)
		tmp = fma(Float64(Float64(z - t) / Float64(a - t)), Float64(y - x), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end
code[x_, y_, z_, t_, a_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-266], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
\begin{array}{l}
t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\
\mathbf{if}\;t_1 \leq -1 \cdot 10^{-266}:\\
\;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\

\mathbf{elif}\;t_1 \leq 0:\\
\;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\


\end{array}

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Herbie found 18 alternatives:

AlternativeAccuracySpeedup

Accuracy vs Speed

The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Bogosity?

Bogosity

Target

Original67.4%
Target86.3%
Herbie90.3%
\[\begin{array}{l} \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array} \]

Derivation?

  1. Split input into 3 regimes
  2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.9999999999999998e-267

    1. Initial program 75.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
    2. Simplified89.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]
      Step-by-step derivation

      [Start]75.2%

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

      +-commutative [=>]75.2%

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

      associate-*r/ [<=]89.2%

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

      *-commutative [<=]89.2%

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

      fma-def [=>]89.2%

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

    if -9.9999999999999998e-267 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

    1. Initial program 3.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
    2. Simplified3.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]
      Step-by-step derivation

      [Start]3.8%

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

      +-commutative [=>]3.8%

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

      associate-*r/ [<=]3.8%

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

      *-commutative [<=]3.8%

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

      fma-def [=>]3.8%

      \[ \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]
    3. Taylor expanded in t around inf 99.9%

      \[\leadsto \color{blue}{y + \frac{\left(-1 \cdot z - -1 \cdot a\right) \cdot \left(y - x\right)}{t}} \]
    4. Simplified99.9%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]
      Step-by-step derivation

      [Start]99.9%

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

      *-commutative [<=]99.9%

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

      cancel-sign-sub-inv [=>]99.9%

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

      metadata-eval [=>]99.9%

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

      *-lft-identity [=>]99.9%

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

      distribute-lft-in [=>]99.9%

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

      mul-1-neg [=>]99.9%

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

      distribute-rgt-neg-in [<=]99.9%

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

      mul-1-neg [<=]99.9%

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

      *-commutative [<=]99.9%

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

      cancel-sign-sub [<=]99.9%

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

      mul-1-neg [<=]99.9%

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

      associate-*r* [<=]99.9%

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

      distribute-lft-out-- [=>]99.9%

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

      associate-*r/ [<=]99.9%

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

      mul-1-neg [=>]99.9%

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

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

    1. Initial program 67.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
    2. Simplified91.5%

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

      [Start]67.2%

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

      associate-/l* [=>]91.5%

      \[ x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]
  3. Recombined 3 regimes into one program.
  4. Final simplification91.2%

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-266}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy90.3%
Cost8004
\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-266}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]
Alternative 2
Accuracy90.4%
Cost2633
\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-266} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(x - y\right) \cdot \frac{t - z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]
Alternative 3
Accuracy90.3%
Cost2632
\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-266}:\\ \;\;\;\;x + \left(x - y\right) \cdot \frac{t - z}{a - t}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]
Alternative 4
Accuracy46.0%
Cost1504
\[\begin{array}{l} t_1 := x - x \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -1.06 \cdot 10^{+53}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3900000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-81}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-199}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-278}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 190000000:\\ \;\;\;\;\frac{t - z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
Alternative 5
Accuracy46.3%
Cost1504
\[\begin{array}{l} t_1 := x - x \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+54}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -23000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-81}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-202}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-278}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 102000000:\\ \;\;\;\;\frac{y \cdot \left(t - z\right)}{t}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
Alternative 6
Accuracy64.9%
Cost1369
\[\begin{array}{l} t_1 := x - x \cdot \frac{z}{a}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1.12 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -122000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-91}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 200000000 \lor \neg \left(t \leq 1.1 \cdot 10^{+73}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 7
Accuracy37.9%
Cost1244
\[\begin{array}{l} t_1 := \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+50}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -0.182:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
Alternative 8
Accuracy39.9%
Cost1240
\[\begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ t_2 := x + \frac{x \cdot z}{a}\\ \mathbf{if}\;t \leq -1 \cdot 10^{+57}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -100000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1020:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
Alternative 9
Accuracy47.6%
Cost1240
\[\begin{array}{l} t_1 := x - x \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -9 \cdot 10^{+58}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -19000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-81}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-202}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-278}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
Alternative 10
Accuracy72.9%
Cost1234
\[\begin{array}{l} \mathbf{if}\;t \leq -3.05 \cdot 10^{+53} \lor \neg \left(t \leq 1.5 \cdot 10^{-86} \lor \neg \left(t \leq 2.25 \cdot 10^{-34}\right) \land t \leq 6 \cdot 10^{+71}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a - t}\\ \end{array} \]
Alternative 11
Accuracy56.3%
Cost1104
\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+148}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-207}:\\ \;\;\;\;\frac{-z}{\frac{a - t}{x}}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+179}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x \cdot z}{a}\\ \end{array} \]
Alternative 12
Accuracy38.7%
Cost980
\[\begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+53}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -45000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-129}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-41}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
Alternative 13
Accuracy49.4%
Cost976
\[\begin{array}{l} t_1 := x - x \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+51}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -35000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-81}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
Alternative 14
Accuracy66.3%
Cost972
\[\begin{array}{l} t_1 := \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-86}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{t}}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 15
Accuracy78.9%
Cost969
\[\begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+62} \lor \neg \left(t \leq 4.1 \cdot 10^{-84}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a - t}\\ \end{array} \]
Alternative 16
Accuracy37.9%
Cost328
\[\begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+176}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 17
Accuracy2.8%
Cost64
\[0 \]
Alternative 18
Accuracy25.3%
Cost64
\[x \]

Reproduce?

herbie shell --seed 2023272 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))