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

Average Error: 24.4 → 9.8

Time: 32.6s

Precision: binary64

Cost: 1096

Math

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

↓

\[\begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{-209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-180}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 (+ x (* (- t x) (/ (- y z) (- a z))))))
   (if (<= a -1.02e-209)
     t_1
     (if (<= a 2.2e-180) (- t (/ (- t x) (/ z y))) t_1))))

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 = x + ((t - x) * ((y - z) / (a - z)));
	double tmp;
	if (a <= -1.02e-209) {
		tmp = t_1;
	} else if (a <= 2.2e-180) {
		tmp = t - ((t - x) / (z / y));
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = x + ((t - x) * ((y - z) / (a - z)))
    if (a <= (-1.02d-209)) then
        tmp = t_1
    else if (a <= 2.2d-180) then
        tmp = t - ((t - x) / (z / y))
    else
        tmp = t_1
    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 = x + ((t - x) * ((y - z) / (a - z)));
	double tmp;
	if (a <= -1.02e-209) {
		tmp = t_1;
	} else if (a <= 2.2e-180) {
		tmp = t - ((t - x) / (z / y));
	} else {
		tmp = t_1;
	}
	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 = x + ((t - x) * ((y - z) / (a - z)))
	tmp = 0
	if a <= -1.02e-209:
		tmp = t_1
	elif a <= 2.2e-180:
		tmp = t - ((t - x) / (z / y))
	else:
		tmp = t_1
	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(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))))
	tmp = 0.0
	if (a <= -1.02e-209)
		tmp = t_1;
	elseif (a <= 2.2e-180)
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / y)));
	else
		tmp = t_1;
	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 = x + ((t - x) * ((y - z) / (a - z)));
	tmp = 0.0;
	if (a <= -1.02e-209)
		tmp = t_1;
	elseif (a <= 2.2e-180)
		tmp = t - ((t - x) / (z / y));
	else
		tmp = t_1;
	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[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.02e-209], t$95$1, If[LessEqual[a, 2.2e-180], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Target

Original	24.4
Target	11.9
Herbie	9.8

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

Derivation

1. Split input into 2 regimes

2. if a < -1.01999999999999999e-209 or 2.20000000000000013e-180 < a

   1. Initial program 23.5

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

   2. Simplified 10.4

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

      [Start] 23.5	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      rational.json-simplify-49 [=>] 10.4	\[ x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} \]

   if -1.01999999999999999e-209 < a < 2.20000000000000013e-180

   1. Initial program 28.9

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

   2. Simplified 19.5

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

      [Start] 28.9	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      rational.json-simplify-49 [=>] 19.5	\[ x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} \]

   3. Taylor expanded in z around -inf 9.4

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

   4. Simplified 9.4

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

      [Start] 9.4	\[ -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z} + t \]
      rational.json-simplify-1 [=>] 9.4	\[ \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
      rational.json-simplify-2 [=>] 9.4	\[ t + \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z} \cdot -1} \]
      rational.json-simplify-9 [=>] 9.4	\[ t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]
      rational.json-simplify-2 [=>] 9.4	\[ t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot y} - a \cdot \left(t - x\right)}{z}\right) \]
      rational.json-simplify-52 [=>] 9.4	\[ t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

   5. Taylor expanded in a around 0 11.0

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

   6. Simplified 6.7

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

      [Start] 11.0	\[ t - \frac{y \cdot \left(t - x\right)}{z} \]
      rational.json-simplify-49 [=>] 6.8	\[ t - \color{blue}{\left(t - x\right) \cdot \frac{y}{z}} \]
      rational.json-simplify-2 [=>] 6.8	\[ t - \color{blue}{\frac{y}{z} \cdot \left(t - x\right)} \]
      rational.json-simplify-35 [=>] 6.8	\[ t - \color{blue}{\frac{y + y}{z + z}} \cdot \left(t - x\right) \]
      rational.json-simplify-7 [<=] 6.8	\[ t - \frac{y + y}{\color{blue}{\frac{z + z}{1}}} \cdot \left(t - x\right) \]
      rational.json-simplify-61 [=>] 6.9	\[ t - \color{blue}{\frac{1}{\frac{z + z}{y + y}}} \cdot \left(t - x\right) \]
      rational.json-simplify-7 [<=] 6.9	\[ t - \frac{1}{\frac{z + z}{y + y}} \cdot \color{blue}{\frac{t - x}{1}} \]
      rational.json-simplify-55 [=>] 6.7	\[ t - \color{blue}{\frac{\frac{t - x}{1}}{\frac{\frac{z + z}{y + y}}{1}}} \]
      rational.json-simplify-7 [=>] 6.7	\[ t - \frac{\color{blue}{t - x}}{\frac{\frac{z + z}{y + y}}{1}} \]
      rational.json-simplify-7 [=>] 6.7	\[ t - \frac{t - x}{\color{blue}{\frac{z + z}{y + y}}} \]
      rational.json-simplify-36 [=>] 6.7	\[ t - \frac{t - x}{\color{blue}{\frac{z}{y}}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 9.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{-209}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-180}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternatives

Alternative 1
Error	29.7
Cost	1504

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t - a \cdot \frac{x}{z}\\ t_3 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-80}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-269}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+36}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	30.5
Cost	1504

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ t_2 := t - a \cdot \frac{x}{z}\\ t_3 := t - y \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+101}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{+18}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-166}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-269}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.02 \cdot 10^{-193}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	30.6
Cost	1504

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ t_2 := t - a \cdot \frac{x}{z}\\ t_3 := t - y \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+18}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-166}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-269}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-193}:\\ \;\;\;\;x + y \cdot \left(-\frac{x}{a}\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	31.0
Cost	1504

\[\begin{array}{l} t_1 := t - y \cdot \frac{t}{z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.72 \cdot 10^{+81}:\\ \;\;\;\;x + z \cdot \left(-\frac{t}{a}\right)\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-269}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-193}:\\ \;\;\;\;x + y \cdot \left(-\frac{x}{a}\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \]

Alternative 5
Error	23.5
Cost	1368

\[\begin{array}{l} \mathbf{if}\;a \leq -2300000000000:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-61}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-79}:\\ \;\;\;\;\frac{y \cdot x}{z - a}\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-107}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a} + x\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-89}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(-x\right)\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{+147}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \end{array} \]

Alternative 6
Error	22.5
Cost	1368

\[\begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;a \leq -35000000000000:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-61}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-88}:\\ \;\;\;\;\frac{y \cdot x}{z - a}\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-107}:\\ \;\;\;\;\frac{t_1}{a} + x\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-89}:\\ \;\;\;\;t - \frac{t_1}{z}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+148}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \end{array} \]

Alternative 7
Error	31.7
Cost	1240

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.62 \cdot 10^{+174}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-269}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{a}{z} + 1\right)\\ \end{array} \]

Alternative 8
Error	31.8
Cost	1240

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.62 \cdot 10^{+174}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-80}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-269}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{a}{z} + 1\right)\\ \end{array} \]

Alternative 9
Error	31.7
Cost	1240

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -1.62 \cdot 10^{+174}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-80}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-269}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+44}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{a}{z} + 1\right)\\ \end{array} \]

Alternative 10
Error	31.8
Cost	1240

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -1.62 \cdot 10^{+174}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-269}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{a}{z} + 1\right)\\ \end{array} \]

Alternative 11
Error	23.5
Cost	1236

\[\begin{array}{l} \mathbf{if}\;a \leq -4800000000000:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-61}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-107}:\\ \;\;\;\;\frac{y \cdot x}{z - a}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-89}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(-x\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+147}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \end{array} \]

Alternative 12
Error	15.3
Cost	1232

\[\begin{array}{l} t_1 := x + t \cdot \frac{z - y}{z - a}\\ \mathbf{if}\;a \leq -7 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-107}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a} + x\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-107}:\\ \;\;\;\;x + z \cdot \left(-\frac{t}{a}\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-110}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	23.7
Cost	1104

\[\begin{array}{l} t_1 := x + t \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -1800000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-61}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-107}:\\ \;\;\;\;\frac{y \cdot x}{z - a}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-89}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	23.7
Cost	1104

\[\begin{array}{l} \mathbf{if}\;a \leq -17000000000000:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-61}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-107}:\\ \;\;\;\;\frac{y \cdot x}{z - a}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-39}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]

Alternative 15
Error	24.1
Cost	1104

\[\begin{array}{l} \mathbf{if}\;a \leq -8000000000000:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -1.04 \cdot 10^{-50}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-107}:\\ \;\;\;\;\frac{y \cdot x}{z - a}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-89}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 16
Error	27.1
Cost	1040

\[\begin{array}{l} \mathbf{if}\;a \leq -41000000000000:\\ \;\;\;\;x + z \cdot \left(-\frac{t}{a}\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-61}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-70}:\\ \;\;\;\;\frac{y \cdot x}{z - a}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-89}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 17
Error	19.8
Cost	972

\[\begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+26}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-89}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+147}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \end{array} \]

Alternative 18
Error	35.0
Cost	712

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-71}:\\ \;\;\;\;t \cdot \left(\frac{a}{z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	36.4
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -2.35 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-66}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20
Error	45.8
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023074 
(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))))