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

Average Accuracy: 69.2% → 88.5%

Time: 33.1s

Precision: binary64

Cost: 8004

Math

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

↓

\[\begin{array}{l} t_1 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-290}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{a - y}{\frac{-z}{x}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+300}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \end{array} \]

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 (/ (* (- y z) (- x t)) (- a z)))))
   (if (<= t_1 -1e-290)
     (fma (/ (- y z) (- a z)) (- t x) x)
     (if (<= t_1 0.0)
       (+ t (/ (- a y) (/ (- z) x)))
       (if (<= t_1 2e+300) t_1 (+ t (/ (- a y) (/ z (- t x)))))))))

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 - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if (t_1 <= -1e-290) {
		tmp = fma(((y - z) / (a - z)), (t - x), x);
	} else if (t_1 <= 0.0) {
		tmp = t + ((a - y) / (-z / x));
	} else if (t_1 <= 2e+300) {
		tmp = t_1;
	} else {
		tmp = t + ((a - y) / (z / (t - x)));
	}
	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(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= -1e-290)
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), Float64(t - x), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(a - y) / Float64(Float64(-z) / x)));
	elseif (t_1 <= 2e+300)
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(a - y) / Float64(z / Float64(t - x))));
	end
	return 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[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-290], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(a - y), $MachinePrecision] / N[((-z) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+300], t$95$1, N[(t + N[(N[(a - y), $MachinePrecision] / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	69.2%
Target	84.2%
Herbie	88.5%

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

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.0000000000000001e-290

   1. Initial program 72.2%

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

   2. Simplified 92.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]
      Step-by-step derivation

      [Start] 72.2	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      +-commutative [=>] 72.2	\[ \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]
      associate-*l/ [<=] 92.5	\[ \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]
      fma-def [=>] 92.5	\[ \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   if -1.0000000000000001e-290 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.4%

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

   2. Simplified 4.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]
      Step-by-step derivation

      [Start] 4.4	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      +-commutative [=>] 4.4	\[ \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]
      associate-*l/ [<=] 4.4	\[ \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]
      fma-def [=>] 4.4	\[ \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Taylor expanded in z around inf 99.9%

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

   4. Simplified 99.9%

      \[\leadsto \color{blue}{t - \frac{y - a}{\frac{z}{t - x}}} \]
      Step-by-step derivation

      [Start] 99.9	\[ \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t \]
      +-commutative [=>] 99.9	\[ \color{blue}{t + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}} \]
      distribute-lft-out-- [=>] 99.9	\[ t + \frac{\color{blue}{\left(-1 \cdot \left(y - a\right)\right)} \cdot \left(t - x\right)}{z} \]
      associate-*r* [<=] 99.9	\[ t + \frac{\color{blue}{-1 \cdot \left(\left(y - a\right) \cdot \left(t - x\right)\right)}}{z} \]
      mul-1-neg [=>] 99.9	\[ t + \frac{\color{blue}{-\left(y - a\right) \cdot \left(t - x\right)}}{z} \]
      distribute-neg-frac [<=] 99.9	\[ t + \color{blue}{\left(-\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 99.9	\[ \color{blue}{t - \frac{\left(y - a\right) \cdot \left(t - x\right)}{z}} \]
      associate-/l* [=>] 99.9	\[ t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   5. Taylor expanded in t around 0 99.9%

      \[\leadsto t - \frac{y - a}{\color{blue}{-1 \cdot \frac{z}{x}}} \]

   6. Simplified 99.9%

      \[\leadsto t - \frac{y - a}{\color{blue}{\frac{-z}{x}}} \]
      Step-by-step derivation

      [Start] 99.9	\[ t - \frac{y - a}{-1 \cdot \frac{z}{x}} \]
      associate-*r/ [=>] 99.9	\[ t - \frac{y - a}{\color{blue}{\frac{-1 \cdot z}{x}}} \]
      neg-mul-1 [<=] 99.9	\[ t - \frac{y - a}{\frac{\color{blue}{-z}}{x}} \]

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 2.0000000000000001e300

   1. Initial program 96.4%

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

   if 2.0000000000000001e300 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 30.0%

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

   2. Simplified 66.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]
      Step-by-step derivation

      [Start] 30.0	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      +-commutative [=>] 30.0	\[ \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]
      associate-*l/ [<=] 66.9	\[ \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]
      fma-def [=>] 66.9	\[ \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   3. Taylor expanded in z around inf 61.0%

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

   4. Simplified 78.9%

      \[\leadsto \color{blue}{t - \frac{y - a}{\frac{z}{t - x}}} \]
      Step-by-step derivation

      [Start] 61.0	\[ \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z} + t \]
      +-commutative [=>] 61.0	\[ \color{blue}{t + \frac{\left(-1 \cdot y - -1 \cdot a\right) \cdot \left(t - x\right)}{z}} \]
      distribute-lft-out-- [=>] 61.0	\[ t + \frac{\color{blue}{\left(-1 \cdot \left(y - a\right)\right)} \cdot \left(t - x\right)}{z} \]
      associate-*r* [<=] 61.0	\[ t + \frac{\color{blue}{-1 \cdot \left(\left(y - a\right) \cdot \left(t - x\right)\right)}}{z} \]
      mul-1-neg [=>] 61.0	\[ t + \frac{\color{blue}{-\left(y - a\right) \cdot \left(t - x\right)}}{z} \]
      distribute-neg-frac [<=] 61.0	\[ t + \color{blue}{\left(-\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 61.0	\[ \color{blue}{t - \frac{\left(y - a\right) \cdot \left(t - x\right)}{z}} \]
      associate-/l* [=>] 78.9	\[ t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

3. Recombined 4 regimes into one program.

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -1 \cdot 10^{-290}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{elif}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{a - y}{\frac{-z}{x}}\\ \mathbf{elif}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 2 \cdot 10^{+300}:\\ \;\;\;\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	88.5%
Cost	3532

\[\begin{array}{l} t_1 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-290}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a - z}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{a - y}{\frac{-z}{x}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+300}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \end{array} \]

Alternative 2
Accuracy	56.0%
Cost	1764

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := y \cdot \frac{t - x}{a - z}\\ t_3 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;y \leq -3900:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.12 \cdot 10^{-187}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-249}:\\ \;\;\;\;x \cdot \left(\frac{z}{a - z} + 1\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-199}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{-132}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-107}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 175:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	38.1%
Cost	1372

\[\begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{+26}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-271}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-210}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4
Accuracy	48.9%
Cost	1372

\[\begin{array}{l} t_1 := \frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{if}\;a \leq -33000:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.82 \cdot 10^{-68}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-88}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-96}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-126}:\\ \;\;\;\;x \cdot \frac{-y}{a - z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 5
Accuracy	61.0%
Cost	1372

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -4.3 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-159}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 6
Accuracy	37.1%
Cost	1244

\[\begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -5 \cdot 10^{+26}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-142}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-287}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-210}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7
Accuracy	37.1%
Cost	1244

\[\begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+24}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-142}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-289}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-269}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-209}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+77}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8
Accuracy	37.1%
Cost	1244

\[\begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+27}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-144}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-297}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-271}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-211}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9
Accuracy	37.1%
Cost	1244

\[\begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+28}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-269}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-210}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10
Accuracy	44.9%
Cost	1240

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+28}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-227}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-96}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11
Accuracy	43.4%
Cost	1240

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{-80}:\\ \;\;\;\;\frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq -3.05 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-222}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-97}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12
Accuracy	71.4%
Cost	1232

\[\begin{array}{l} t_1 := t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{x - t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-74}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+73}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Accuracy	88.6%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+82} \lor \neg \left(z \leq 8.8 \cdot 10^{+189}\right):\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a - z}\\ \end{array} \]

Alternative 14
Accuracy	50.5%
Cost	976

\[\begin{array}{l} t_1 := \frac{t}{z} \cdot \left(z - y\right)\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.95 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-239}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Accuracy	50.4%
Cost	976

\[\begin{array}{l} t_1 := \frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{-28}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-239}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 16
Accuracy	65.9%
Cost	973

\[\begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+70}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-74} \lor \neg \left(z \leq 1.35 \cdot 10^{+76}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 17
Accuracy	65.1%
Cost	973

\[\begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+70}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-75} \lor \neg \left(z \leq 5 \cdot 10^{+73}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 18
Accuracy	72.2%
Cost	969

\[\begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-75} \lor \neg \left(z \leq 5 \cdot 10^{+73}\right):\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 19
Accuracy	71.9%
Cost	968

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-73}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+73}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a - y}{\frac{z}{t - x}}\\ \end{array} \]

Alternative 20
Accuracy	68.2%
Cost	904

\[\begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-75}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+87}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a - y}{\frac{-z}{x}}\\ \end{array} \]

Alternative 21
Accuracy	54.3%
Cost	844

\[\begin{array}{l} t_1 := t - a \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-73}:\\ \;\;\;\;\frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+90}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 22
Accuracy	49.9%
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+203}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-74}:\\ \;\;\;\;\frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+86}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \]

Alternative 23
Accuracy	55.8%
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+71}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-73}:\\ \;\;\;\;\frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+88}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \]

Alternative 24
Accuracy	66.7%
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-74}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+76}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 25
Accuracy	37.9%
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+25}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 26
Accuracy	24.8%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023159 
(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))))