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

Average Accuracy: 62.2% → 89.5%

Time: 29.7s

Precision: binary64

Cost: 4432

Math

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

↓

\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t_1 \leq -4 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+302}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - x}{a - t} \cdot \left(t - z\right)\\ \end{array} \]

FPCore

(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 (- INFINITY))
     (+ y (* (- z a) (/ (- x y) t)))
     (if (<= t_1 -4e-293)
       t_1
       (if (<= t_1 0.0)
         (+ y (/ (* (- y x) (- a z)) t))
         (if (<= t_1 2e+302) t_1 (- x (* (/ (- y x) (- a t)) (- t z)))))))))

C

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 <= -((double) INFINITY)) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else if (t_1 <= -4e-293) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_1 <= 2e+302) {
		tmp = t_1;
	} else {
		tmp = x - (((y - x) / (a - t)) * (t - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}

↓

public static 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 <= -Double.POSITIVE_INFINITY) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else if (t_1 <= -4e-293) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_1 <= 2e+302) {
		tmp = t_1;
	} else {
		tmp = x - (((y - x) / (a - t)) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	return x + (((y - x) * (z - t)) / (a - t))

↓

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y + ((z - a) * ((x - y) / t))
	elif t_1 <= -4e-293:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y + (((y - x) * (a - z)) / t)
	elif t_1 <= 2e+302:
		tmp = t_1
	else:
		tmp = x - (((y - x) / (a - t)) * (t - z))
	return tmp

Julia

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 <= Float64(-Inf))
		tmp = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)));
	elseif (t_1 <= -4e-293)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t_1 <= 2e+302)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(Float64(y - x) / Float64(a - t)) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (((y - x) * (z - t)) / (a - t));
end

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y + ((z - a) * ((x - y) / t));
	elseif (t_1 <= -4e-293)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (t_1 <= 2e+302)
		tmp = t_1;
	else
		tmp = x - (((y - x) / (a - t)) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

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, (-Infinity)], N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -4e-293], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+302], t$95$1, N[(x - N[(N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	62.2%
Target	85.7%
Herbie	89.5%

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

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0

   1. Initial program 0.0%

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

   2. Simplified 73.3%

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

      [Start] 0.0	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      +-commutative [=>] 0.0	\[ \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]
      associate-*r/ [<=] 73.3	\[ \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]
      *-commutative [<=] 73.3	\[ \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]
      fma-def [=>] 73.3	\[ \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Taylor expanded in t around inf 36.8%

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

   4. Simplified 69.3%

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

      [Start] 36.8	\[ y + \frac{\left(-1 \cdot z - -1 \cdot a\right) \cdot \left(y - x\right)}{t} \]
      distribute-lft-out-- [=>] 36.8	\[ y + \frac{\color{blue}{\left(-1 \cdot \left(z - a\right)\right)} \cdot \left(y - x\right)}{t} \]
      associate-*r* [<=] 36.8	\[ y + \frac{\color{blue}{-1 \cdot \left(\left(z - a\right) \cdot \left(y - x\right)\right)}}{t} \]
      *-commutative [<=] 36.8	\[ y + \frac{-1 \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - a\right)\right)}}{t} \]
      associate-*r/ [<=] 36.8	\[ y + \color{blue}{-1 \cdot \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]
      mul-1-neg [=>] 36.8	\[ y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)} \]
      unsub-neg [=>] 36.8	\[ \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]
      associate-/l* [=>] 68.4	\[ y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]
      associate-/r/ [=>] 69.3	\[ y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.0000000000000002e-293 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 2.0000000000000002e302

   1. Initial program 97.2%

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

   if -4.0000000000000002e-293 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 6.5%

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

   2. Simplified 6.5%

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

      [Start] 6.5	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      +-commutative [=>] 6.5	\[ \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]
      associate-*r/ [<=] 6.5	\[ \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]
      *-commutative [<=] 6.5	\[ \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]
      fma-def [=>] 6.5	\[ \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Taylor expanded in t around inf 97.6%

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

   4. Simplified 90.5%

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

      [Start] 97.6	\[ y + \frac{\left(-1 \cdot z - -1 \cdot a\right) \cdot \left(y - x\right)}{t} \]
      distribute-lft-out-- [=>] 97.6	\[ y + \frac{\color{blue}{\left(-1 \cdot \left(z - a\right)\right)} \cdot \left(y - x\right)}{t} \]
      associate-*r* [<=] 97.6	\[ y + \frac{\color{blue}{-1 \cdot \left(\left(z - a\right) \cdot \left(y - x\right)\right)}}{t} \]
      *-commutative [<=] 97.6	\[ y + \frac{-1 \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - a\right)\right)}}{t} \]
      associate-*r/ [<=] 97.6	\[ y + \color{blue}{-1 \cdot \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]
      mul-1-neg [=>] 97.6	\[ y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)} \]
      unsub-neg [=>] 97.6	\[ \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]
      associate-/l* [=>] 97.7	\[ y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]
      associate-/r/ [=>] 90.5	\[ y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Taylor expanded in t around 0 97.6%

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

   if 2.0000000000000002e302 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 2.0%

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

   2. Simplified 71.8%

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

      [Start] 2.0	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      associate-*l/ [<=] 71.8	\[ x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

3. Recombined 4 regimes into one program.

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{-293}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 2 \cdot 10^{+302}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - x}{a - t} \cdot \left(t - z\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	42.8%
Cost	1372

\[\begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+45}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-33}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-39}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-238}:\\ \;\;\;\;x \cdot \left(1 + \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-83}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 0.08:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+225}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 2
Accuracy	53.8%
Cost	1368

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := \left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-285}:\\ \;\;\;\;x \cdot \left(1 + \frac{t}{a - t}\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-64}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	53.6%
Cost	1368

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.64 \cdot 10^{-285}:\\ \;\;\;\;x \cdot \left(1 + \frac{t}{a - t}\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-64}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Accuracy	45.0%
Cost	1240

\[\begin{array}{l} t_1 := x - t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9 \cdot 10^{+112}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-203}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 3.65 \cdot 10^{-90}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+15}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Accuracy	43.1%
Cost	1108

\[\begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-39}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-238}:\\ \;\;\;\;x \cdot \left(1 + \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-185}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 0.00047:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+225}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 6
Accuracy	42.3%
Cost	1108

\[\begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-39}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-240}:\\ \;\;\;\;x \cdot \left(1 + \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-81}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+225}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7
Accuracy	62.7%
Cost	1104

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(1 + \frac{t - z}{a - t}\right)\\ \mathbf{elif}\;a \leq 1.48 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Accuracy	83.7%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-154} \lor \neg \left(a \leq 2.6 \cdot 10^{-104}\right):\\ \;\;\;\;x - \frac{y - x}{a - t} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]

Alternative 9
Accuracy	87.9%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+85} \lor \neg \left(t \leq 2.6 \cdot 10^{+154}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternative 10
Accuracy	50.6%
Cost	1041

\[\begin{array}{l} t_1 := x - t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9 \cdot 10^{+112}:\\ \;\;\;\;\frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -3.15 \cdot 10^{+72} \lor \neg \left(a \leq 1.9 \cdot 10^{+16}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \end{array} \]

Alternative 11
Accuracy	50.1%
Cost	977

\[\begin{array}{l} t_1 := x - t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.7 \cdot 10^{+112}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{+73} \lor \neg \left(a \leq 6.5 \cdot 10^{+15}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 12
Accuracy	50.0%
Cost	977

\[\begin{array}{l} t_1 := x - t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{+176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9 \cdot 10^{+112}:\\ \;\;\;\;\frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{+74} \lor \neg \left(a \leq 10^{+16}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 13
Accuracy	68.1%
Cost	969

\[\begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{-39} \lor \neg \left(t \leq 1.25 \cdot 10^{+53}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 14
Accuracy	74.5%
Cost	969

\[\begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-39} \lor \neg \left(t \leq 9.8 \cdot 10^{+42}\right):\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 15
Accuracy	75.1%
Cost	969

\[\begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-39} \lor \neg \left(t \leq 8.2 \cdot 10^{+42}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 16
Accuracy	57.4%
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+180} \lor \neg \left(a \leq 2.6 \cdot 10^{+16}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 17
Accuracy	66.0%
Cost	841

\[\begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-48} \lor \neg \left(t \leq 0.165\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \end{array} \]

Alternative 18
Accuracy	66.0%
Cost	841

\[\begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-48} \lor \neg \left(t \leq 0.105\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 19
Accuracy	42.5%
Cost	716

\[\begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{-39}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-184}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 78:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 20
Accuracy	42.5%
Cost	716

\[\begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-39}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-238}:\\ \;\;\;\;x \cdot \left(1 + \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-185}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 5.8:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 21
Accuracy	42.0%
Cost	592

\[\begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+172}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{+112}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+16}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22
Accuracy	43.2%
Cost	328

\[\begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-39}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 0.0076:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 23
Accuracy	28.7%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023141 
(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))))