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

Average Accuracy: 62.2% → 89.1%

Time: 32.4s

Precision: binary64

Cost: 8004

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y - z}{a - z}\\ t_2 := x - \frac{\left(t - x\right) \cdot \left(z - y\right)}{a - z}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-305}:\\ \;\;\;\;\mathsf{fma}\left(t_1, t - x, x\right)\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot t_1\\ \end{array} \]

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 (/ (- y z) (- a z))) (t_2 (- x (/ (* (- t x) (- z y)) (- a z)))))
   (if (<= t_2 -2e-305)
     (fma t_1 (- t x) x)
     (if (<= t_2 0.0) (+ t (/ (* (- t x) (- a y)) z)) (+ x (* (- t x) 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 = (y - z) / (a - z);
	double t_2 = x - (((t - x) * (z - y)) / (a - z));
	double tmp;
	if (t_2 <= -2e-305) {
		tmp = fma(t_1, (t - x), x);
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((t - x) * 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(Float64(y - z) / Float64(a - z))
	t_2 = Float64(x - Float64(Float64(Float64(t - x) * Float64(z - y)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -2e-305)
		tmp = fma(t_1, Float64(t - x), x);
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	else
		tmp = Float64(x + Float64(Float64(t - x) * t_1));
	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[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(N[(t - x), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-305], N[(t$95$1 * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	62.2%
Target	81.4%
Herbie	89.1%

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

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.99999999999999999e-305

   1. Initial program 68.0%

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

   2. Simplified 88.8%

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

      [Start] 68.0	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      +-commutative [=>] 68.0	\[ \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x} \]
      associate-*l/ [<=] 88.8	\[ \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} + x \]
      fma-def [=>] 88.8	\[ \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]

   if -1.99999999999999999e-305 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.6%

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

   2. Simplified 4.3%

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

      [Start] 4.6	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      associate-/l* [=>] 4.3	\[ x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   3. Taylor expanded in z around inf 99.5%

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

   4. Simplified 99.5%

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

      [Start] 99.5	\[ \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + t\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      +-commutative [=>] 99.5	\[ \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right)} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      associate--l+ [=>] 99.5	\[ \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]
      associate-*r/ [=>] 99.5	\[ t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]
      associate-*r/ [=>] 99.5	\[ t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]
      div-sub [<=] 99.5	\[ t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]
      distribute-lft-out-- [=>] 99.5	\[ t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]
      associate-*r/ [<=] 99.5	\[ t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
      mul-1-neg [=>] 99.5	\[ t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 99.5	\[ \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
      distribute-rgt-out-- [=>] 99.5	\[ t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

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

   1. Initial program 67.0%

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

   2. Simplified 87.5%

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

      [Start] 67.0	\[ x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
      associate-*l/ [<=] 87.5	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(t - x\right) \cdot \left(z - y\right)}{a - z} \leq -2 \cdot 10^{-305}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{elif}\;x - \frac{\left(t - x\right) \cdot \left(z - y\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	89.1%
Cost	2633

\[\begin{array}{l} t_1 := x - \frac{\left(t - x\right) \cdot \left(z - y\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-305} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 2
Accuracy	58.6%
Cost	2552

\[\begin{array}{l} t_1 := x - \frac{z \cdot t}{a - z}\\ t_2 := t + \frac{y \cdot \left(x - t\right)}{z}\\ t_3 := t \cdot \frac{y - z}{a - z}\\ t_4 := \frac{t}{\frac{a - z}{y - z}}\\ t_5 := x \cdot \left(1 + \frac{z - y}{a - z}\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+92}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{+65}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-21}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-275}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-300}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-250}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 10^{-206}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-6}:\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y}}\\ \mathbf{elif}\;t \leq 600000:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+177}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+191}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 3
Accuracy	54.6%
Cost	2425

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ t_3 := t + x \cdot \frac{y}{z}\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-300}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-222}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-207}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-39}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-10}:\\ \;\;\;\;\frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 16000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+184} \lor \neg \left(t \leq 2.1 \cdot 10^{+191}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 4
Accuracy	54.4%
Cost	1896

\[\begin{array}{l} t_1 := t + x \cdot \frac{y}{z}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ t_3 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -9.8 \cdot 10^{+145}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{+14}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-42}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-264}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-288}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2600000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+121}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+171}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 5
Accuracy	61.9%
Cost	1633

\[\begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -1.12 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{+25}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -310000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-231}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 6800:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+121} \lor \neg \left(a \leq 6.4 \cdot 10^{+173}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Accuracy	33.0%
Cost	1504

\[\begin{array}{l} t_1 := y \cdot \frac{t}{a - z}\\ \mathbf{if}\;x \leq -3.15 \cdot 10^{+230}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-60}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-121}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-234}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-79}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Accuracy	57.5%
Cost	1500

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-264}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-288}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3100:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+121}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+171}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Accuracy	61.6%
Cost	1500

\[\begin{array}{l} t_1 := x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{+22}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -53000000:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-147}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-263}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{-286}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 0.038:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Accuracy	53.5%
Cost	1241

\[\begin{array}{l} t_1 := t - t \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+216}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+129}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2600000:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+87} \lor \neg \left(z \leq 6.5 \cdot 10^{+144}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 10
Accuracy	53.4%
Cost	1241

\[\begin{array}{l} t_1 := t - t \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+216}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.24 \cdot 10^{+129}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 780000:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+89} \lor \neg \left(z \leq 6.5 \cdot 10^{+144}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 11
Accuracy	77.5%
Cost	1232

\[\begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t}}\\ t_2 := t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{+75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-170}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Accuracy	43.5%
Cost	1120

\[\begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+216}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+181}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+18}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-152}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-137}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1300000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+87}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+144}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13
Accuracy	43.2%
Cost	1120

\[\begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+216}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+19}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-152}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-140}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 950000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+87}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+144}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14
Accuracy	60.0%
Cost	1108

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := t + x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{-34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 0.61:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+136}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Accuracy	68.7%
Cost	1104

\[\begin{array}{l} t_1 := x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{+21}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -7.1 \cdot 10^{-43}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 2800:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Accuracy	68.5%
Cost	1104

\[\begin{array}{l} t_1 := x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{+23}:\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-45}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 320000:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Accuracy	52.8%
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+216}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+181}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+19}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+144}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18
Accuracy	55.8%
Cost	976

\[\begin{array}{l} t_1 := t - t \cdot \frac{y}{z}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-198}:\\ \;\;\;\;y \cdot \frac{x}{z - a}\\ \mathbf{elif}\;a \leq 6000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 19
Accuracy	76.5%
Cost	969

\[\begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-48} \lor \neg \left(a \leq 5.8 \cdot 10^{-64}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y}{z}\\ \end{array} \]

Alternative 20
Accuracy	43.7%
Cost	856

\[\begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+216}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+181}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 290000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+87}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+144}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 21
Accuracy	44.9%
Cost	592

\[\begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+19}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2300000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+88}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+145}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 22
Accuracy	29.6%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023137 
(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))))