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

Average Error: 24.5 → 6.0

Time: 31.5s

Precision: binary64

Cost: 4432

Math

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

↓

\[\begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ t_2 := x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-294}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+289}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 (* (- z t) (/ (- y x) (- a t)))))
        (t_2 (+ x (/ (* (- x y) (- t z)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e-294)
       t_2
       (if (<= t_2 0.0)
         (+ y (/ (- x y) (/ t (- z a))))
         (if (<= t_2 5e+289) t_2 t_1))))))

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 + ((z - t) * ((y - x) / (a - t)));
	double t_2 = x + (((x - y) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e-294) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else if (t_2 <= 5e+289) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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 + ((z - t) * ((y - x) / (a - t)));
	double t_2 = x + (((x - y) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e-294) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else if (t_2 <= 5e+289) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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 + ((z - t) * ((y - x) / (a - t)))
	t_2 = x + (((x - y) * (t - z)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e-294:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + ((x - y) / (t / (z - a)))
	elif t_2 <= 5e+289:
		tmp = t_2
	else:
		tmp = t_1
	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(z - t) * Float64(Float64(y - x) / Float64(a - t))))
	t_2 = Float64(x + Float64(Float64(Float64(x - y) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e-294)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	elseif (t_2 <= 5e+289)
		tmp = t_2;
	else
		tmp = t_1;
	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 + ((z - t) * ((y - x) / (a - t)));
	t_2 = x + (((x - y) * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e-294)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + ((x - y) / (t / (z - a)));
	elseif (t_2 <= 5e+289)
		tmp = t_2;
	else
		tmp = t_1;
	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[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(x - y), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e-294], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+289], t$95$2, t$95$1]]]]]]

Target

Original	24.5
Target	8.6
Herbie	6.0

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

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 5.00000000000000031e289 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 62.4

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

   2. Simplified 16.0

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

      [Start] 62.4	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      associate-*l/ [<=] 16.0	\[ x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.0000000000000003e-294 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 5.00000000000000031e289

   1. Initial program 2.0

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

   if -5.0000000000000003e-294 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 60.5

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

   2. Simplified 60.5

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

      [Start] 60.5	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      +-commutative [=>] 60.5	\[ \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]
      associate-*l/ [<=] 60.8	\[ \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]
      fma-def [=>] 60.5	\[ \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Taylor expanded in t around -inf 1.2

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

   4. Simplified 1.0

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

      [Start] 1.2	\[ y + -1 \cdot \frac{-1 \cdot \left(a \cdot \left(y - x\right)\right) + z \cdot \left(y - x\right)}{t} \]
      mul-1-neg [=>] 1.2	\[ y + \color{blue}{\left(-\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right) + z \cdot \left(y - x\right)}{t}\right)} \]
      unsub-neg [=>] 1.2	\[ \color{blue}{y - \frac{-1 \cdot \left(a \cdot \left(y - x\right)\right) + z \cdot \left(y - x\right)}{t}} \]
      +-commutative [=>] 1.2	\[ y - \frac{\color{blue}{z \cdot \left(y - x\right) + -1 \cdot \left(a \cdot \left(y - x\right)\right)}}{t} \]
      associate-*r* [=>] 1.2	\[ y - \frac{z \cdot \left(y - x\right) + \color{blue}{\left(-1 \cdot a\right) \cdot \left(y - x\right)}}{t} \]
      distribute-rgt-out [=>] 1.2	\[ y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z + -1 \cdot a\right)}}{t} \]
      associate-/l* [=>] 1.0	\[ y - \color{blue}{\frac{y - x}{\frac{t}{z + -1 \cdot a}}} \]
      mul-1-neg [=>] 1.0	\[ y - \frac{y - x}{\frac{t}{z + \color{blue}{\left(-a\right)}}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 6.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq -5 \cdot 10^{-294}:\\ \;\;\;\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq 5 \cdot 10^{+289}:\\ \;\;\;\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternatives

Alternative 1
Error	6.3
Cost	2633

\[\begin{array}{l} t_1 := x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-294} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]

Alternative 2
Error	23.3
Cost	1628

\[\begin{array}{l} t_1 := x \cdot \left(1 + \frac{t - z}{a - t}\right)\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{z - t}{\frac{a - t}{y}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+140}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \end{array} \]

Alternative 3
Error	23.3
Cost	1628

\[\begin{array}{l} t_1 := x - \frac{x}{\frac{a - t}{z - t}}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-92}:\\ \;\;\;\;\frac{z - t}{\frac{a - t}{y}}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+138}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \end{array} \]

Alternative 4
Error	22.5
Cost	1497

\[\begin{array}{l} t_1 := x \cdot \left(1 + \frac{t - z}{a - t}\right)\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -2.75 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-92}:\\ \;\;\;\;\frac{z - t}{\frac{a - t}{y}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+69} \lor \neg \left(t \leq 2.6 \cdot 10^{+98}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	18.5
Cost	1496

\[\begin{array}{l} t_1 := y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{if}\;t \leq -6.6 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1750000000000:\\ \;\;\;\;x \cdot \left(1 + \frac{t - z}{a - t}\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-7}:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+68}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+98}:\\ \;\;\;\;x - \frac{x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	33.0
Cost	1304

\[\begin{array}{l} t_1 := y \cdot \frac{-t}{a - t}\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-83}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-46}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+120}:\\ \;\;\;\;\frac{-z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7
Error	32.3
Cost	1304

\[\begin{array}{l} t_1 := y \cdot \frac{-t}{a - t}\\ \mathbf{if}\;t \leq -3.15 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-83}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-46}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+69}:\\ \;\;\;\;\frac{z - t}{\frac{-t}{y}}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	36.6
Cost	1240

\[\begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+111}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-46}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+61}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+122}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9
Error	34.1
Cost	1240

\[\begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+110}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-83}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-46}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+62}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+120}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 10
Error	33.0
Cost	1240

\[\begin{array}{l} t_1 := y \cdot \frac{-t}{a - t}\\ \mathbf{if}\;t \leq -1.58 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-84}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-45}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+121}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 11
Error	36.6
Cost	1176

\[\begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+106}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-46}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+64}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+69}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 12
Error	34.1
Cost	1176

\[\begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+106}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-83}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-46}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+66}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+68}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 13
Error	28.3
Cost	1105

\[\begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \left(1 - \frac{t}{t - a}\right)\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{+51} \lor \neg \left(x \leq -1.55 \cdot 10^{-20}\right) \land x \leq 1.8 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \end{array} \]

Alternative 14
Error	28.4
Cost	1104

\[\begin{array}{l} t_1 := x - \frac{z}{\frac{a}{x}}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -3.15 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-100}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	10.3
Cost	1097

\[\begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+146} \lor \neg \left(t \leq 1.9 \cdot 10^{+107}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 16
Error	26.7
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+154} \lor \neg \left(a \leq 1.05 \cdot 10^{+108}\right):\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 17
Error	22.9
Cost	841

\[\begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+61} \lor \neg \left(t \leq 2.85 \cdot 10^{-25}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \]

Alternative 18
Error	22.0
Cost	841

\[\begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+61} \lor \neg \left(t \leq 5.3 \cdot 10^{-25}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 19
Error	36.2
Cost	716

\[\begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+108}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-46}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 20
Error	36.3
Cost	716

\[\begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+107}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-46}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 21
Error	36.2
Cost	716

\[\begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+106}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-46}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 22
Error	35.8
Cost	328

\[\begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+106}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 23
Error	45.3
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023060 
(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))))