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

Average Error: 24.3 → 9.9

Time: 23.5s

Precision: binary64

Cost: 1097

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-89} \lor \neg \left(a \leq 1.6 \cdot 10^{+26}\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ (* (- y z) (- t x)) (- a z))))

↓

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.4e-89) (not (<= a 1.6e+26)))
   (+ x (* (/ (- y z) (- a z)) (- t x)))
   (- t (/ (- t x) (/ z (- y a))))))

C

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 tmp;
	if ((a <= -1.4e-89) || !(a <= 1.6e+26)) {
		tmp = x + (((y - z) / (a - z)) * (t - x));
	} else {
		tmp = t - ((t - x) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (((y - z) * (t - x)) / (a - z))
end function

↓

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.4d-89)) .or. (.not. (a <= 1.6d+26))) then
        tmp = x + (((y - z) / (a - z)) * (t - x))
    else
        tmp = t - ((t - x) / (z / (y - a)))
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.4e-89) || !(a <= 1.6e+26)) {
		tmp = x + (((y - z) / (a - z)) * (t - x));
	} else {
		tmp = t - ((t - x) / (z / (y - a)));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.4e-89) or not (a <= 1.6e+26):
		tmp = x + (((y - z) / (a - z)) * (t - x))
	else:
		tmp = t - ((t - x) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
end

↓

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.4e-89) || !(a <= 1.6e+26))
		tmp = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * Float64(t - x)));
	else
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.4e-89) || ~((a <= 1.6e+26)))
		tmp = x + (((y - z) / (a - z)) * (t - x));
	else
		tmp = t - ((t - x) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.4e-89], N[Not[LessEqual[a, 1.6e+26]], $MachinePrecision]], N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	24.3
Target	12.4
Herbie	9.9

\[\begin{array}{l} \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if a < -1.3999999999999999e-89 or 1.60000000000000014e26 < a

   1. Initial program 22.0

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

   2. Simplified 7.3

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

      [Start] 22.0	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      associate-*l/ [<=] 7.3	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   if -1.3999999999999999e-89 < a < 1.60000000000000014e26

   1. Initial program 27.4

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

   2. Simplified 18.2

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

      [Start] 27.4	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      associate-*l/ [<=] 18.2	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Taylor expanded in z around inf 18.7

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

   4. Simplified 13.5

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

      [Start] 18.7	\[ \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + t\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      +-commutative [=>] 18.7	\[ \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right)} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      associate--l+ [=>] 18.7	\[ \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]
      associate-*r/ [=>] 18.7	\[ t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]
      associate-*r/ [=>] 18.7	\[ t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]
      div-sub [<=] 18.7	\[ t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]
      distribute-lft-out-- [=>] 18.7	\[ t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]
      associate-*r/ [<=] 18.7	\[ t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
      mul-1-neg [=>] 18.7	\[ t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 18.7	\[ \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
      distribute-rgt-out-- [=>] 18.7	\[ t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]
      associate-/l* [=>] 13.5	\[ t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 9.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-89} \lor \neg \left(a \leq 1.6 \cdot 10^{+26}\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \]

Alternatives

Alternative 1
Error	32.7
Cost	1768

\[\begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ t_2 := x - x \cdot \frac{y}{a}\\ t_3 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+104}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{+84}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{+55}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-37}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-151}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-188}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+46}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	32.6
Cost	1768

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_3 := x + \frac{y \cdot t}{a}\\ t_4 := \frac{t}{\frac{z - a}{z}}\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{+139}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+104}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{+83}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{+26}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-37}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-188}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	32.6
Cost	1768

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_3 := x + \frac{y \cdot t}{a}\\ t_4 := \frac{t}{\frac{z - a}{z}}\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{+139}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{+102}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{+83}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{+29}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-37}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-188}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	32.6
Cost	1768

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_3 := x + \frac{y \cdot t}{a}\\ t_4 := \frac{t}{\frac{z - a}{z}}\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{+139}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{+104}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{+83}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{+21}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-37}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-188}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{a - z}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	29.8
Cost	1765

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;t \leq -3.55 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.58 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-306}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq 4.65 \cdot 10^{-296}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-234}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-81} \lor \neg \left(t \leq 4.6 \cdot 10^{-25}\right) \land t \leq 1.8 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	31.6
Cost	1504

\[\begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+104}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{+84}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.1 \cdot 10^{-151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-188}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	19.5
Cost	1496

\[\begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{+139}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{+103}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-37}:\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-85}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+26}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	18.8
Cost	1364

\[\begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a - y}{z}\\ t_2 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -5.8 \cdot 10^{+139}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{+97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-8}:\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	33.9
Cost	1240

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{+139}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{+84}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-188}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Error	33.5
Cost	976

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -1.76 \cdot 10^{+139}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-188}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Error	33.6
Cost	976

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{+139}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-188}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Error	36.4
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-150}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Error	21.9
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -0.008 \lor \neg \left(z \leq 4.5 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 14
Error	22.0
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-15} \lor \neg \left(z \leq 4 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]

Alternative 15
Error	36.2
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16
Error	45.8
Cost	64

\[t \]

Reproduce

herbie shell --seed 2022364 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

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