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

Average Accuracy: 62.0% → 86.5%

Time: 28.7s

Precision: binary64

Cost: 1097

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-101} \lor \neg \left(a \leq 5 \cdot 10^{-103}\right):\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

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 -8e-101) (not (<= a 5e-103)))
   (+ x (* (- x t) (/ (- z y) (- a z))))
   (+ t (/ (- x t) (/ 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 <= -8e-101) || !(a <= 5e-103)) {
		tmp = x + ((x - t) * ((z - y) / (a - z)));
	} else {
		tmp = t + ((x - t) / (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 <= (-8d-101)) .or. (.not. (a <= 5d-103))) then
        tmp = x + ((x - t) * ((z - y) / (a - z)))
    else
        tmp = t + ((x - t) / (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 <= -8e-101) || !(a <= 5e-103)) {
		tmp = x + ((x - t) * ((z - y) / (a - z)));
	} else {
		tmp = t + ((x - t) / (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 <= -8e-101) or not (a <= 5e-103):
		tmp = x + ((x - t) * ((z - y) / (a - z)))
	else:
		tmp = t + ((x - t) / (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 <= -8e-101) || !(a <= 5e-103))
		tmp = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / 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 <= -8e-101) || ~((a <= 5e-103)))
		tmp = x + ((x - t) * ((z - y) / (a - z)));
	else
		tmp = t + ((x - t) / (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, -8e-101], N[Not[LessEqual[a, 5e-103]], $MachinePrecision]], N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	62.0%
Target	81.2%
Herbie	86.5%

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

Derivation

1. Split input into 2 regimes

2. if a < -8.00000000000000041e-101 or 4.99999999999999966e-103 < a

   1. Initial program 64.3%

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

   2. Simplified 86.5%

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

      [Start] 64.3	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      associate-*l/ [<=] 86.5	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   if -8.00000000000000041e-101 < a < 4.99999999999999966e-103

   1. Initial program 56.5%

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

   2. Simplified 70.9%

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

      [Start] 56.5	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      associate-*l/ [<=] 70.9	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Taylor expanded in z around inf 79.3%

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

   4. Simplified 86.6%

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

      [Start] 79.3	\[ \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + t\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      +-commutative [=>] 79.3	\[ \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right)} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      associate--l+ [=>] 79.3	\[ \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]
      associate-*r/ [=>] 79.3	\[ t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]
      associate-*r/ [=>] 79.3	\[ t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]
      div-sub [<=] 79.3	\[ t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]
      distribute-lft-out-- [=>] 79.3	\[ t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]
      associate-*r/ [<=] 79.3	\[ t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
      mul-1-neg [=>] 79.3	\[ t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 79.3	\[ \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
      distribute-rgt-out-- [=>] 79.3	\[ t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]
      associate-/l* [=>] 86.6	\[ t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-101} \lor \neg \left(a \leq 5 \cdot 10^{-103}\right):\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	53.6%
Cost	1632

\[\begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;a \leq -9.2 \cdot 10^{+204}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{+162}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.7 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+185}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Accuracy	53.6%
Cost	1632

\[\begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;a \leq -2 \cdot 10^{+205}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+162}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+190}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{z}{a - z}\right)\\ \end{array} \]

Alternative 3
Accuracy	46.7%
Cost	1504

\[\begin{array}{l} \mathbf{if}\;a \leq -3.65 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \frac{-x}{a - z}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-9}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+52}:\\ \;\;\;\;\frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+69}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a - z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+155}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+206}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Accuracy	54.3%
Cost	1368

\[\begin{array}{l} t_1 := \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;a \leq -6.8 \cdot 10^{+204}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \frac{-x}{a - z}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Accuracy	41.5%
Cost	1240

\[\begin{array}{l} t_1 := \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -9.8 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-259}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-10}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+14}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{+18}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Accuracy	41.3%
Cost	1240

\[\begin{array}{l} t_1 := t + \frac{a \cdot t}{z}\\ t_2 := \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -6.9 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-167}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+14}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+17}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Accuracy	47.3%
Cost	1240

\[\begin{array}{l} \mathbf{if}\;a \leq -150000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-9}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+19}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+155}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+206}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Accuracy	47.1%
Cost	1240

\[\begin{array}{l} t_1 := t - t \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -29000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+53}:\\ \;\;\;\;\frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+155}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+207}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Accuracy	47.0%
Cost	1240

\[\begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 10^{-9}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+52}:\\ \;\;\;\;\frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+70}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a - z}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+153}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+206}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Accuracy	70.9%
Cost	1232

\[\begin{array}{l} t_1 := x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -4500000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-48}:\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-70}:\\ \;\;\;\;x + \frac{z}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+20}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Accuracy	68.3%
Cost	1104

\[\begin{array}{l} t_1 := x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-48}:\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-9}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Accuracy	68.6%
Cost	1104

\[\begin{array}{l} t_1 := x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -340000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-48}:\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-70}:\\ \;\;\;\;x + \frac{z}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-10}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Accuracy	72.2%
Cost	1100

\[\begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+39}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+26}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Accuracy	68.8%
Cost	972

\[\begin{array}{l} t_1 := t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+52}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Accuracy	43.5%
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-112}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16
Accuracy	65.6%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+39} \lor \neg \left(z \leq 9.8 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 17
Accuracy	48.9%
Cost	716

\[\begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-9}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Accuracy	44.1%
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+40}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19
Accuracy	28.2%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023151 
(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))))