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

Average Accuracy: 60.8% → 89.3%

Time: 30.4s

Precision: binary64

Cost: 9160

Math

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

↓

\[\begin{array}{l} t_1 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-294}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a - z}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y - a}{z}, t + \frac{t}{z} \cdot \left(a - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]

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 -5e-294)
     (- x (* (- t x) (/ (- z y) (- a z))))
     (if (<= t_1 0.0)
       (fma x (/ (- y a) z) (+ t (* (/ t z) (- a y))))
       (+ x (/ (- t x) (/ (- a z) (- y z))))))))

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 <= -5e-294) {
		tmp = x - ((t - x) * ((z - y) / (a - z)));
	} else if (t_1 <= 0.0) {
		tmp = fma(x, ((y - a) / z), (t + ((t / z) * (a - y))));
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	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 <= -5e-294)
		tmp = Float64(x - Float64(Float64(t - x) * Float64(Float64(z - y) / Float64(a - z))));
	elseif (t_1 <= 0.0)
		tmp = fma(x, Float64(Float64(y - a) / z), Float64(t + Float64(Float64(t / z) * Float64(a - y))));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	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, -5e-294], N[(x - N[(N[(t - x), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] + N[(t + N[(N[(t / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	60.8%
Target	81.5%
Herbie	89.3%

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

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5.0000000000000003e-294

   1. Initial program 65.3%

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

   2. Simplified 88.2%

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

      [Start] 65.3	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      associate-*l/ [<=] 88.2	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   if -5.0000000000000003e-294 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 5.9%

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

   2. Simplified 5.9%

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

      [Start] 5.9	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      associate-*l/ [<=] 5.9	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Applied egg-rr 5.9%

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

      [Start] 5.9	\[ x + \frac{y - z}{a - z} \cdot \left(t - x\right) \]
      *-commutative [=>] 5.9	\[ x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} \]
      clear-num [=>] 5.9	\[ x + \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} \]
      un-div-inv [=>] 5.9	\[ x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   4. Taylor expanded in z around inf 98.0%

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

   5. Simplified 98.1%

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

      [Start] 98.0	\[ \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + t\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      +-commutative [=>] 98.0	\[ \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right)} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      associate--l+ [=>] 98.0	\[ \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]
      associate-*r/ [=>] 98.0	\[ t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]
      associate-*r/ [=>] 98.0	\[ t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]
      div-sub [<=] 98.0	\[ t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]
      distribute-lft-out-- [=>] 98.0	\[ t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]
      associate-*r/ [<=] 98.0	\[ t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
      mul-1-neg [=>] 98.0	\[ t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 98.0	\[ \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
      distribute-rgt-out-- [=>] 98.0	\[ t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]
      associate-/l* [=>] 98.1	\[ t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in x around 0 98.0%

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

   7. Simplified 98.1%

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

      [Start] 98.0	\[ \left(\frac{\left(y - a\right) \cdot x}{z} + t\right) - \frac{t \cdot \left(y - a\right)}{z} \]
      associate--l+ [=>] 98.0	\[ \color{blue}{\frac{\left(y - a\right) \cdot x}{z} + \left(t - \frac{t \cdot \left(y - a\right)}{z}\right)} \]
      *-commutative [=>] 98.0	\[ \frac{\color{blue}{x \cdot \left(y - a\right)}}{z} + \left(t - \frac{t \cdot \left(y - a\right)}{z}\right) \]
      associate-*r/ [<=] 98.2	\[ \color{blue}{x \cdot \frac{y - a}{z}} + \left(t - \frac{t \cdot \left(y - a\right)}{z}\right) \]
      associate-*l/ [<=] 98.1	\[ x \cdot \frac{y - a}{z} + \left(t - \color{blue}{\frac{t}{z} \cdot \left(y - a\right)}\right) \]
      fma-def [=>] 98.1	\[ \color{blue}{\mathsf{fma}\left(x, \frac{y - a}{z}, t - \frac{t}{z} \cdot \left(y - a\right)\right)} \]
      *-commutative [=>] 98.1	\[ \mathsf{fma}\left(x, \frac{y - a}{z}, t - \color{blue}{\left(y - a\right) \cdot \frac{t}{z}}\right) \]

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

   1. Initial program 66.6%

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

   2. Simplified 88.6%

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

      [Start] 66.6	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      associate-*l/ [<=] 88.6	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Applied egg-rr 88.7%

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

      [Start] 88.6	\[ x + \frac{y - z}{a - z} \cdot \left(t - x\right) \]
      *-commutative [=>] 88.6	\[ x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} \]
      clear-num [=>] 88.5	\[ x + \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} \]
      un-div-inv [=>] 88.7	\[ x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -5 \cdot 10^{-294}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a - z}\\ \mathbf{elif}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 0:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y - a}{z}, t + \frac{t}{z} \cdot \left(a - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	89.3%
Cost	2633

\[\begin{array}{l} t_1 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-294} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 2
Accuracy	89.3%
Cost	2632

\[\begin{array}{l} t_1 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-294}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a - z}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 3
Accuracy	50.1%
Cost	1900

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -7 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-28}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-32}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-197}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -3.25 \cdot 10^{-223}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-185}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-134}:\\ \;\;\;\;\frac{y}{\frac{z - a}{x}}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-52}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.8:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 1450000:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+157}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	49.7%
Cost	1900

\[\begin{array}{l} t_1 := \frac{t \cdot \left(z - y\right)}{z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-27}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-33}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-193}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-223}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-134}:\\ \;\;\;\;\frac{y}{\frac{z - a}{x}}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-48}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.35:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 1100000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+157}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Accuracy	49.6%
Cost	1900

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -8.6 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-24}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-39}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-197}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-223}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-181}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-134}:\\ \;\;\;\;\frac{y}{\frac{z - a}{x}}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-49}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.25:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 1300000:\\ \;\;\;\;\frac{-z \cdot t}{a - z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+157}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Accuracy	51.0%
Cost	1764

\[\begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;y \leq -2.65 \cdot 10^{+203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+184}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-46}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-84}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-223}:\\ \;\;\;\;x + \frac{t}{-\frac{a}{z}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-132}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	50.8%
Cost	1636

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-28}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-32}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-197}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -8.3 \cdot 10^{-224}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-48}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 0.49:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 48000000:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+157}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	53.6%
Cost	1636

\[\begin{array}{l} t_1 := \frac{t}{-\frac{z}{y - z}}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.15 \cdot 10^{-223}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-134}:\\ \;\;\;\;\frac{y}{\frac{z - a}{x}}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.55:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 60000000:\\ \;\;\;\;\frac{-z \cdot t}{a - z}\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{+157}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Accuracy	52.9%
Cost	1636

\[\begin{array}{l} t_1 := \frac{t}{\frac{z - a}{z}}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-223}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 10^{-180}:\\ \;\;\;\;\frac{t}{-\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-134}:\\ \;\;\;\;\frac{y}{\frac{z - a}{x}}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 0.28:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 880000:\\ \;\;\;\;\frac{-z \cdot t}{a - z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+157}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Accuracy	62.1%
Cost	1633

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -2.55 \cdot 10^{+45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.35 \cdot 10^{-223}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-134}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-48} \lor \neg \left(a \leq 0.26\right) \land a \leq 1.3 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Accuracy	62.7%
Cost	1633

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{+44}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.35 \cdot 10^{-223}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-48} \lor \neg \left(a \leq 0.25\right) \land a \leq 3 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]

Alternative 12
Accuracy	59.1%
Cost	1632

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -6.7 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.25 \cdot 10^{-223}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-134}:\\ \;\;\;\;\frac{y}{\frac{z - a}{x}}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 0.25:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Accuracy	68.5%
Cost	1500

\[\begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y}}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -1.22 \cdot 10^{+48}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-177}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-48}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 0.86:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2300000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{+47}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+123}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Accuracy	68.5%
Cost	1500

\[\begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y}}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -8.7 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-177}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-48}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 0.25:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 640000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{t}{-\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Accuracy	38.8%
Cost	1372

\[\begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.85 \cdot 10^{+186}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-265}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-173}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+157}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Accuracy	49.9%
Cost	1372

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -4 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-182}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-224}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-49}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 0.27:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 900000:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+157}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Accuracy	79.0%
Cost	1232

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y - z}}\\ t_2 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-188}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Accuracy	77.7%
Cost	969

\[\begin{array}{l} \mathbf{if}\;a \leq -1.42 \cdot 10^{-131} \lor \neg \left(a \leq 1.05 \cdot 10^{-84}\right):\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \]

Alternative 19
Accuracy	48.7%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20
Accuracy	44.4%
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 21
Accuracy	29.5%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023135 
(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))))