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

Average Error: 24.0 → 6.6

Time: 27.7s

Precision: binary64

Cost: 4432

Math

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

↓

\[\begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-278}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y - \frac{x \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t_2 \leq 10^{+273}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e-278)
       t_2
       (if (<= t_2 0.0)
         (- y (/ (* x (- a z)) t))
         (if (<= t_2 1e+273) 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 + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e-278) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - ((x * (a - z)) / t);
	} else if (t_2 <= 1e+273) {
		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 + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e-278) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - ((x * (a - z)) / t);
	} else if (t_2 <= 1e+273) {
		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 + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e-278:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y - ((x * (a - z)) / t)
	elif t_2 <= 1e+273:
		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(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e-278)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y - Float64(Float64(x * Float64(a - z)) / t));
	elseif (t_2 <= 1e+273)
		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 + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e-278)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y - ((x * (a - z)) / t);
	elseif (t_2 <= 1e+273)
		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[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e-278], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y - N[(N[(x * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+273], t$95$2, t$95$1]]]]]]

Target

Original	24.0
Target	9.4
Herbie	6.6

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

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 9.99999999999999945e272 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 60.7

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

   2. Simplified 17.5

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

      [Start] 60.7	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      associate-*l/ [<=] 17.5	\[ x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.99999999999999985e-278 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.99999999999999945e272

   1. Initial program 2.0

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

   if -4.99999999999999985e-278 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 58.4

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

   2. Simplified 58.3

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

      [Start] 58.4	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      associate-/l* [=>] 58.3	\[ x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Taylor expanded in t around inf 3.0

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

   4. Simplified 3.0

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

      [Start] 3.0	\[ \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + y\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t} \]
      +-commutative [=>] 3.0	\[ \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right)} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t} \]
      associate--l+ [=>] 3.0	\[ \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]
      *-commutative [=>] 3.0	\[ y + \left(-1 \cdot \frac{\color{blue}{\left(y - x\right) \cdot z}}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]
      associate-*r/ [=>] 3.0	\[ y + \left(\color{blue}{\frac{-1 \cdot \left(\left(y - x\right) \cdot z\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]
      associate-*r/ [=>] 3.0	\[ y + \left(\frac{-1 \cdot \left(\left(y - x\right) \cdot z\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]
      div-sub [<=] 3.0	\[ y + \color{blue}{\frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]
      distribute-lft-out-- [=>] 3.0	\[ y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z - a \cdot \left(y - x\right)\right)}}{t} \]
      *-commutative [<=] 3.0	\[ y + \frac{-1 \cdot \left(\color{blue}{z \cdot \left(y - x\right)} - a \cdot \left(y - x\right)\right)}{t} \]
      distribute-rgt-out-- [=>] 3.0	\[ y + \frac{-1 \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - a\right)\right)}}{t} \]
      associate-*r* [=>] 3.0	\[ y + \frac{\color{blue}{\left(-1 \cdot \left(y - x\right)\right) \cdot \left(z - a\right)}}{t} \]
      mul-1-neg [=>] 3.0	\[ y + \frac{\color{blue}{\left(-\left(y - x\right)\right)} \cdot \left(z - a\right)}{t} \]
      neg-sub0 [=>] 3.0	\[ y + \frac{\color{blue}{\left(0 - \left(y - x\right)\right)} \cdot \left(z - a\right)}{t} \]
      associate-+l- [<=] 3.0	\[ y + \frac{\color{blue}{\left(\left(0 - y\right) + x\right)} \cdot \left(z - a\right)}{t} \]
      neg-sub0 [<=] 3.0	\[ y + \frac{\left(\color{blue}{\left(-y\right)} + x\right) \cdot \left(z - a\right)}{t} \]
      +-commutative [<=] 3.0	\[ y + \frac{\color{blue}{\left(x + \left(-y\right)\right)} \cdot \left(z - a\right)}{t} \]
      unsub-neg [=>] 3.0	\[ y + \frac{\color{blue}{\left(x - y\right)} \cdot \left(z - a\right)}{t} \]

   5. Taylor expanded in x around inf 2.9

      \[\leadsto y + \color{blue}{\frac{\left(z - a\right) \cdot x}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 6.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-278}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{x \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 10^{+273}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternatives

Alternative 1
Error	31.1
Cost	2160

\[\begin{array}{l} t_1 := x - \frac{x \cdot z}{a}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ t_3 := x + \frac{y \cdot z}{a}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{-106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-175}:\\ \;\;\;\;x - z \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-187}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-304}:\\ \;\;\;\;\frac{-z}{\frac{a - t}{x}}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-233}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-180}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-130}:\\ \;\;\;\;z \cdot \frac{x}{t - a}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-106}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-105}:\\ \;\;\;\;\frac{-z}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+111}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	30.7
Cost	1764

\[\begin{array}{l} t_1 := x + \frac{y \cdot z}{a}\\ t_2 := \frac{t}{a - t} \cdot \left(-y\right)\\ t_3 := \left(y - x\right) \cdot \frac{z}{a - t}\\ t_4 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;z \leq -8500000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-111}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-169}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-277}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-119}:\\ \;\;\;\;x + \frac{t}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+75}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 3
Error	30.4
Cost	1764

\[\begin{array}{l} t_1 := x + \frac{y \cdot z}{a}\\ t_2 := \frac{t}{a - t} \cdot \left(-y\right)\\ t_3 := \left(y - x\right) \cdot \frac{z}{a - t}\\ t_4 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;z \leq -7800000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-111}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-170}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-277}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-222}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-170}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-116}:\\ \;\;\;\;x + \frac{t}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+77}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Error	30.2
Cost	1764

\[\begin{array}{l} t_1 := x + \frac{y \cdot z}{a}\\ t_2 := \frac{t}{a - t} \cdot \left(-y\right)\\ t_3 := \left(y - x\right) \cdot \frac{z}{a - t}\\ t_4 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;z \leq -59000000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.25 \cdot 10^{-111}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-170}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-277}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-222}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-174}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.04 \cdot 10^{-131}:\\ \;\;\;\;x + \frac{t}{\frac{a - t}{x}}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+73}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 5
Error	37.7
Cost	1637

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{a}\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+135}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 10^{-72}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \frac{x}{t - a}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+58}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+123} \lor \neg \left(a \leq 3.4 \cdot 10^{+160}\right) \land a \leq 8.8 \cdot 10^{+202}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	38.0
Cost	1637

\[\begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{+156}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+83}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-73}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \frac{x}{t - a}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+63}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+122} \lor \neg \left(a \leq 8 \cdot 10^{+159}\right) \land a \leq 9.2 \cdot 10^{+202}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	38.0
Cost	1637

\[\begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+156}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{+80}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-73}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-30}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+60}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{+122} \lor \neg \left(a \leq 2.15 \cdot 10^{+162}\right) \land a \leq 8.8 \cdot 10^{+202}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	38.1
Cost	1636

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{a}\\ t_2 := x + \frac{t}{\frac{a}{x}}\\ \mathbf{if}\;a \leq -4 \cdot 10^{+175}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{+77}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-73}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-30}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+63}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+162}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+203}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	34.7
Cost	1636

\[\begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{z}{t}\\ t_2 := x + \frac{y \cdot z}{a}\\ \mathbf{if}\;a \leq -5.1 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{+83}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-145}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -3.25 \cdot 10^{-170}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 10^{-72}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+45}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	34.6
Cost	1636

\[\begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{z}{t}\\ t_2 := x + \frac{y \cdot z}{a}\\ \mathbf{if}\;a \leq -5.1 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{+83}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-145}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-170}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-73}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+49}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	22.3
Cost	1500

\[\begin{array}{l} t_1 := y + \left(z - a\right) \cdot \frac{x}{t}\\ t_2 := x + \left(y - x\right) \cdot \frac{z}{a}\\ t_3 := y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -59000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-32}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.38 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-179}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	37.5
Cost	1373

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{a}\\ \mathbf{if}\;a \leq -6.6 \cdot 10^{+134}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+63}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+122} \lor \neg \left(a \leq 2.6 \cdot 10^{+162}\right) \land a \leq 8.8 \cdot 10^{+202}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Error	23.5
Cost	1368

\[\begin{array}{l} t_1 := y + \left(z - a\right) \cdot \frac{x}{t}\\ t_2 := x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-32}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-58}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Error	23.5
Cost	1368

\[\begin{array}{l} t_1 := y + \left(z - a\right) \cdot \frac{x}{t}\\ t_2 := x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.45 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-32}:\\ \;\;\;\;\frac{z - t}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	9.3
Cost	1353

\[\begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+251} \lor \neg \left(t \leq 1.9 \cdot 10^{+92}\right):\\ \;\;\;\;\frac{a}{t} \cdot \left(y - x\right) + \left(y - \frac{z}{\frac{t}{y - x}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternative 16
Error	30.0
Cost	1304

\[\begin{array}{l} t_1 := x + \frac{y \cdot z}{a}\\ t_2 := \frac{t}{a - t} \cdot \left(-y\right)\\ \mathbf{if}\;t \leq -5.7 \cdot 10^{+147}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-54}:\\ \;\;\;\;x - z \cdot \frac{x}{a}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+56}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Error	23.8
Cost	1236

\[\begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{if}\;z \leq -45000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-69}:\\ \;\;\;\;y - \frac{x \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-57}:\\ \;\;\;\;x + \frac{t}{a - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	11.2
Cost	1096

\[\begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+251}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+92}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]

Alternative 19
Error	9.4
Cost	1096

\[\begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+251}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+89}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]

Alternative 20
Error	37.4
Cost	716

\[\begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+148}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.58 \cdot 10^{-254}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-266}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 21
Error	37.1
Cost	592

\[\begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+133}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+111}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22
Error	36.6
Cost	328

\[\begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{+147}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 23
Error	62.1
Cost	64

\[0 \]

Alternative 24
Error	45.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022364 
(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))))