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

Average Error: 37.63% → 13.09%

Time: 30.4s

Precision: binary64

Cost: 1732

Math

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

↓

\[\begin{array}{l} t_1 := \frac{z}{y - a}\\ t_2 := \frac{x - t}{t_1}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+187}:\\ \;\;\;\;\left(t - \frac{a}{\frac{z}{\frac{t - x}{t_1}}}\right) + t_2\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+153}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z} + \left(x + z \cdot \frac{x - t}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t + t_2\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (- y a))) (t_2 (/ (- x t) t_1)))
   (if (<= z -4.6e+187)
     (+ (- t (/ a (/ z (/ (- t x) t_1)))) t_2)
     (if (<= z 1.25e+153)
       (+ (* y (/ (- t x) (- a z))) (+ x (* z (/ (- x t) (- a z)))))
       (+ t t_2)))))

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 t_1 = z / (y - a);
	double t_2 = (x - t) / t_1;
	double tmp;
	if (z <= -4.6e+187) {
		tmp = (t - (a / (z / ((t - x) / t_1)))) + t_2;
	} else if (z <= 1.25e+153) {
		tmp = (y * ((t - x) / (a - z))) + (x + (z * ((x - t) / (a - z))));
	} else {
		tmp = t + t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z / (y - a)
    t_2 = (x - t) / t_1
    if (z <= (-4.6d+187)) then
        tmp = (t - (a / (z / ((t - x) / t_1)))) + t_2
    else if (z <= 1.25d+153) then
        tmp = (y * ((t - x) / (a - z))) + (x + (z * ((x - t) / (a - z))))
    else
        tmp = t + t_2
    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 t_1 = z / (y - a);
	double t_2 = (x - t) / t_1;
	double tmp;
	if (z <= -4.6e+187) {
		tmp = (t - (a / (z / ((t - x) / t_1)))) + t_2;
	} else if (z <= 1.25e+153) {
		tmp = (y * ((t - x) / (a - z))) + (x + (z * ((x - t) / (a - z))));
	} else {
		tmp = t + t_2;
	}
	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):
	t_1 = z / (y - a)
	t_2 = (x - t) / t_1
	tmp = 0
	if z <= -4.6e+187:
		tmp = (t - (a / (z / ((t - x) / t_1)))) + t_2
	elif z <= 1.25e+153:
		tmp = (y * ((t - x) / (a - z))) + (x + (z * ((x - t) / (a - z))))
	else:
		tmp = t + t_2
	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)
	t_1 = Float64(z / Float64(y - a))
	t_2 = Float64(Float64(x - t) / t_1)
	tmp = 0.0
	if (z <= -4.6e+187)
		tmp = Float64(Float64(t - Float64(a / Float64(z / Float64(Float64(t - x) / t_1)))) + t_2);
	elseif (z <= 1.25e+153)
		tmp = Float64(Float64(y * Float64(Float64(t - x) / Float64(a - z))) + Float64(x + Float64(z * Float64(Float64(x - t) / Float64(a - z)))));
	else
		tmp = Float64(t + t_2);
	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)
	t_1 = z / (y - a);
	t_2 = (x - t) / t_1;
	tmp = 0.0;
	if (z <= -4.6e+187)
		tmp = (t - (a / (z / ((t - x) / t_1)))) + t_2;
	elseif (z <= 1.25e+153)
		tmp = (y * ((t - x) / (a - z))) + (x + (z * ((x - t) / (a - z))));
	else
		tmp = t + t_2;
	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_] := Block[{t$95$1 = N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - t), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[z, -4.6e+187], N[(N[(t - N[(a / N[(z / N[(N[(t - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[z, 1.25e+153], N[(N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + N[(z * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + t$95$2), $MachinePrecision]]]]]

Target

Original	37.63%
Target	18.27%
Herbie	13.09%

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

Derivation

1. Split input into 3 regimes

2. if z < -4.60000000000000008e187

   1. Initial program 77.52

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

   2. Simplified 35.38

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

      [Start] 77.52	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      associate-*l/ [<=] 35.38	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Taylor expanded in z around inf 47

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]

   4. Simplified 11.15

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

      [Start] 47	\[ \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      +-commutative [=>] 47	\[ \color{blue}{\left(\left(t + \frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}}\right) + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right)} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      associate--l+ [=>] 47	\[ \color{blue}{\left(t + \frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}}\right) + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

   if -4.60000000000000008e187 < z < 1.25000000000000005e153

   1. Initial program 24.86

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

   2. Simplified 15.35

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

      [Start] 24.86	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      associate-/l* [=>] 15.35	\[ x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   3. Applied egg-rr 13.27

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

   if 1.25000000000000005e153 < z

   1. Initial program 75.38

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

   2. Simplified 35.43

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

      [Start] 75.38	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      associate-*l/ [<=] 35.43	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Taylor expanded in z around inf 37.74

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

   4. Simplified 13.63

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

      [Start] 37.74	\[ \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + t\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      +-commutative [=>] 37.74	\[ \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right)} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      associate--l+ [=>] 37.74	\[ \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]
      associate-*r/ [=>] 37.74	\[ t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]
      associate-*r/ [=>] 37.74	\[ t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]
      div-sub [<=] 37.74	\[ t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]
      distribute-lft-out-- [=>] 37.74	\[ t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]
      associate-*r/ [<=] 37.74	\[ t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
      mul-1-neg [=>] 37.74	\[ t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 37.74	\[ \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
      distribute-rgt-out-- [=>] 37.74	\[ t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]
      associate-/l* [=>] 13.63	\[ t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 13.09

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+187}:\\ \;\;\;\;\left(t - \frac{a}{\frac{z}{\frac{t - x}{\frac{z}{y - a}}}}\right) + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+153}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z} + \left(x + z \cdot \frac{x - t}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternatives

Alternative 1
Error	10.6%
Cost	4432

\[\begin{array}{l} t_1 := x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-281}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;t_1 \leq 10^{-298}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 2
Error	10.61%
Cost	4432

\[\begin{array}{l} t_1 := x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x - \frac{z - y}{\left(a - z\right) \cdot \frac{1}{t - x}}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-281}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;t_1 \leq 10^{-298}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 3
Error	13.09%
Cost	1609

\[\begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+188} \lor \neg \left(z \leq 1.4 \cdot 10^{+153}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z} + \left(x + z \cdot \frac{x - t}{a - z}\right)\\ \end{array} \]

Alternative 4
Error	36.48%
Cost	1500

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -8.6 \cdot 10^{+60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(1 + \frac{z - y}{a - z}\right)\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-125}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-168}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-300}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	33.45%
Cost	1496

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -6 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-125}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{-300}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	49.51%
Cost	1372

\[\begin{array}{l} t_1 := \frac{t}{\frac{z - a}{z}}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -6 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-301}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+70}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+220}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	50.74%
Cost	1372

\[\begin{array}{l} t_1 := \frac{t}{\frac{z - a}{z}}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-300}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-56}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+70}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+220}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	40.42%
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + t \cdot \frac{y}{a}\\ t_3 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;a \leq -6 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.1 \cdot 10^{-168}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-307}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	38.22%
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + y \cdot \frac{t - x}{a}\\ t_3 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.46 \cdot 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-167}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-300}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	37.92%
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;a \leq -5 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-167}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-300}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \end{array} \]

Alternative 11
Error	36.43%
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y - z}}\\ t_3 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-167}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-304}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	36.4%
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y - z}}\\ t_3 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;a \leq -6 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-124}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-167}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-300}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	36.64%
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -5.8 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-122}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-168}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-307}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Error	12.13%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+96} \lor \neg \left(z \leq 2.1 \cdot 10^{+153}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 15
Error	48.68%
Cost	976

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -5 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-255}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-301}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-53}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	28.31%
Cost	969

\[\begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+23} \lor \neg \left(a \leq 10^{-58}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 17
Error	24.76%
Cost	969

\[\begin{array}{l} \mathbf{if}\;a \leq -1.32 \cdot 10^{+20} \lor \neg \left(a \leq 2.7 \cdot 10^{-49}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 18
Error	39.27%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-37} \lor \neg \left(z \leq 6.5 \cdot 10^{-24}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \]

Alternative 19
Error	43.39%
Cost	777

\[\begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+18} \lor \neg \left(a \leq 2.5 \cdot 10^{-46}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{-\frac{z}{y - z}}\\ \end{array} \]

Alternative 20
Error	56.99%
Cost	716

\[\begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-254}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-303}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+135}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21
Error	57.12%
Cost	716

\[\begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-252}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-305}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+135}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22
Error	56.99%
Cost	716

\[\begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-254}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-300}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+135}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 23
Error	56.01%
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 24
Error	71.47%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023088 
(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))))