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

Average Error: 38.23% → 10.96%

Time: 32.2s

Precision: binary64

Cost: 3532

Math

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

↓

\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (+ y (* (/ (- y x) t) (- a z)))
     (if (<= t_1 -2e-298)
       t_1
       (if (<= t_1 0.0)
         (- y (/ (* (- y x) (- z a)) t))
         (+ x (/ (- y x) (/ (- a t) (- z t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}

↓

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (t_1 <= -2e-298) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y - (((y - x) * (z - a)) / t);
	} else {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (t_1 <= -2e-298) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y - (((y - x) * (z - a)) / t);
	} else {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	return x + (((y - x) * (z - t)) / (a - t))

↓

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y + (((y - x) / t) * (a - z))
	elif t_1 <= -2e-298:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y - (((y - x) * (z - a)) / t)
	else:
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
end

↓

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	elseif (t_1 <= -2e-298)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y - Float64(Float64(Float64(y - x) * Float64(z - a)) / t));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (((y - x) * (z - t)) / (a - t));
end

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y + (((y - x) / t) * (a - z));
	elseif (t_1 <= -2e-298)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y - (((y - x) * (z - a)) / t);
	else
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-298], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y - N[(N[(N[(y - x), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	38.23%
Target	14.94%
Herbie	10.96%

\[\begin{array}{l} \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array} \]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0

   1. Initial program 100

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

   2. Simplified 28.18

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

      [Start] 100	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      +-commutative [=>] 100	\[ \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]
      associate-*r/ [<=] 28.2	\[ \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]
      *-commutative [<=] 28.2	\[ \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]
      fma-def [=>] 28.18	\[ \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Taylor expanded in t around inf 62.85

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

   4. Simplified 31.85

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

      [Start] 62.85	\[ y + \frac{\left(-1 \cdot z - -1 \cdot a\right) \cdot \left(y - x\right)}{t} \]
      distribute-lft-out-- [=>] 62.85	\[ y + \frac{\color{blue}{\left(-1 \cdot \left(z - a\right)\right)} \cdot \left(y - x\right)}{t} \]
      associate-*r* [<=] 62.85	\[ y + \frac{\color{blue}{-1 \cdot \left(\left(z - a\right) \cdot \left(y - x\right)\right)}}{t} \]
      *-commutative [<=] 62.85	\[ y + \frac{-1 \cdot \color{blue}{\left(\left(y - x\right) \cdot \left(z - a\right)\right)}}{t} \]
      associate-*r/ [<=] 62.85	\[ y + \color{blue}{-1 \cdot \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]
      mul-1-neg [=>] 62.85	\[ y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)} \]
      unsub-neg [=>] 62.85	\[ \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]
      associate-/l* [=>] 33.41	\[ y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]
      associate-/r/ [=>] 31.85	\[ y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.99999999999999982e-298

   1. Initial program 3.2

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

   if -1.99999999999999982e-298 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 95.18

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

   2. Simplified 95.18

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

      [Start] 95.18	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      associate-/l* [=>] 95.18	\[ x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Taylor expanded in t around inf 0.85

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

   4. Simplified 0.84

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

      [Start] 0.85	\[ \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + y\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t} \]
      +-commutative [=>] 0.85	\[ \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right)} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t} \]
      associate--l+ [=>] 0.84	\[ \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]
      *-commutative [=>] 0.84	\[ y + \left(-1 \cdot \frac{\color{blue}{\left(y - x\right) \cdot z}}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]
      associate-*r/ [=>] 0.84	\[ y + \left(\color{blue}{\frac{-1 \cdot \left(\left(y - x\right) \cdot z\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]
      associate-*r/ [=>] 0.84	\[ y + \left(\frac{-1 \cdot \left(\left(y - x\right) \cdot z\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]
      div-sub [<=] 0.84	\[ y + \color{blue}{\frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]
      distribute-lft-out-- [=>] 0.84	\[ y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z - a \cdot \left(y - x\right)\right)}}{t} \]

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

   1. Initial program 32.68

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

   2. Simplified 11.5

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

      [Start] 32.68	\[ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
      associate-/l* [=>] 11.5	\[ x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

3. Recombined 4 regimes into one program.

4. Final simplification 10.96

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-298}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternatives

Alternative 1
Error	13.4%
Cost	3532

\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 2
Error	47.36%
Cost	1504

\[\begin{array}{l} t_1 := x + x \cdot \frac{t}{a}\\ t_2 := \left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.9 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-33}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+46}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+154}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	47.51%
Cost	1504

\[\begin{array}{l} t_1 := x + x \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -600000000000:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-36}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-112}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+46}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+155}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	31.57%
Cost	1496

\[\begin{array}{l} t_1 := x + \frac{t}{a - t} \cdot \left(x - y\right)\\ t_2 := y + \frac{z - a}{\frac{t}{x}}\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{+204}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+140}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq -205000000:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-186}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	17.29%
Cost	1361

\[\begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+204}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+63} \lor \neg \left(t \leq -0.0175\right) \land t \leq 1.15 \cdot 10^{+66}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \]

Alternative 6
Error	53.85%
Cost	1240

\[\begin{array}{l} t_1 := y - z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -120000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-232}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-250}:\\ \;\;\;\;x + x \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-232}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	53.69%
Cost	1240

\[\begin{array}{l} t_1 := y - z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -145000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-232}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 5.35 \cdot 10^{-250}:\\ \;\;\;\;x + x \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-232}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	53.72%
Cost	1240

\[\begin{array}{l} t_1 := y - z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -200000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-231}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-251}:\\ \;\;\;\;x + x \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-232}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	53.76%
Cost	1240

\[\begin{array}{l} t_1 := y - z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -130000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-232}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-246}:\\ \;\;\;\;x + x \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-232}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	53.67%
Cost	1240

\[\begin{array}{l} t_1 := y - z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -205000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-233}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-247}:\\ \;\;\;\;x + x \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	49.43%
Cost	1240

\[\begin{array}{l} t_1 := y + z \cdot \frac{x}{t}\\ t_2 := x + x \cdot \frac{t}{a}\\ \mathbf{if}\;t \leq -920000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-231}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-250}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-232}:\\ \;\;\;\;\frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+17}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	49.25%
Cost	1240

\[\begin{array}{l} t_1 := x + x \cdot \frac{t}{a}\\ \mathbf{if}\;t \leq -225000000:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-231}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-232}:\\ \;\;\;\;\frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \]

Alternative 13
Error	34.76%
Cost	1236

\[\begin{array}{l} t_1 := x + \left(y - x\right) \cdot \frac{z}{a}\\ t_2 := x - \frac{t}{\frac{a}{y - x}}\\ \mathbf{if}\;a \leq -2.35 \cdot 10^{+191}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+14}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+101}:\\ \;\;\;\;\frac{-z}{\frac{a - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	35.44%
Cost	1236

\[\begin{array}{l} t_1 := x + \left(y - x\right) \cdot \frac{z}{a}\\ t_2 := x - \frac{t}{\frac{a}{y - x}}\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{+189}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 10^{+17}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+140}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	57.12%
Cost	1108

\[\begin{array}{l} \mathbf{if}\;t \leq -23000000000:\\ \;\;\;\;y \cdot \frac{z + t}{t}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -9.4 \cdot 10^{-231}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-253}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-232}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.76 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 16
Error	57.12%
Cost	1108

\[\begin{array}{l} \mathbf{if}\;t \leq -7500000000:\\ \;\;\;\;y \cdot \frac{z + t}{t}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-232}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-253}:\\ \;\;\;\;x + x \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 10^{-231}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 17
Error	30.35%
Cost	1104

\[\begin{array}{l} t_1 := y + \frac{z - a}{\frac{t}{x}}\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.46 \cdot 10^{+143}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq -112000000:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+17}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	27.56%
Cost	1100

\[\begin{array}{l} t_1 := y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{if}\;t \leq -0.00098:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-186}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{t}{a - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	34.54%
Cost	977

\[\begin{array}{l} \mathbf{if}\;t \leq -120000000:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+16}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+138} \lor \neg \left(t \leq 3.8 \cdot 10^{+167}\right):\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y - a \cdot \frac{x}{t}\\ \end{array} \]

Alternative 20
Error	31.84%
Cost	972

\[\begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+251}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-5}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+16}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z - a}{\frac{t}{x}}\\ \end{array} \]

Alternative 21
Error	56.94%
Cost	844

\[\begin{array}{l} \mathbf{if}\;t \leq -21000000000:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-231}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 22
Error	56.99%
Cost	844

\[\begin{array}{l} \mathbf{if}\;t \leq -25000000000:\\ \;\;\;\;y \cdot \frac{z + t}{t}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-233}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 8.3 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 23
Error	34.51%
Cost	840

\[\begin{array}{l} \mathbf{if}\;t \leq -125000000:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+16}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \]

Alternative 24
Error	57.11%
Cost	716

\[\begin{array}{l} \mathbf{if}\;t \leq -25000000000:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-231}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 25
Error	55.65%
Cost	328

\[\begin{array}{l} \mathbf{if}\;t \leq -25000000000:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 26
Error	97.03%
Cost	64

\[0 \]

Alternative 27
Error	71.61%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))