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

Average Error: 24.7 → 5.6

Time: 43.0s

Precision: binary64

Cost: 9220

Math

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

↓

\[\begin{array}{l} t_1 := \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1 + x \cdot \left(\frac{z}{t} + \left(\frac{z}{{t}^{2}} - \frac{1}{t}\right) \cdot a\right)\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-259}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a - t} - \left(\frac{\left(z - t\right) \cdot x}{a - t} - x\right)\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1 + x \cdot \left(-\frac{a - z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + x \cdot \left(\left(2 - \frac{z - t}{a - t}\right) - 1\right)\\ \end{array} \]

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 (* (- (/ z (- a t)) (/ t (- a t))) y))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     (+ t_1 (* x (+ (/ z t) (* (- (/ z (pow t 2.0)) (/ 1.0 t)) a))))
     (if (<= t_2 -5e-259)
       (- (/ (* (- z t) y) (- a t)) (- (/ (* (- z t) x) (- a t)) x))
       (if (<= t_2 0.0)
         (+ t_1 (* x (- (/ (- a z) t))))
         (+ t_1 (* x (- (- 2.0 (/ (- z t) (- a t))) 1.0))))))))

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 = ((z / (a - t)) - (t / (a - t))) * y;
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1 + (x * ((z / t) + (((z / pow(t, 2.0)) - (1.0 / t)) * a)));
	} else if (t_2 <= -5e-259) {
		tmp = (((z - t) * y) / (a - t)) - ((((z - t) * x) / (a - t)) - x);
	} else if (t_2 <= 0.0) {
		tmp = t_1 + (x * -((a - z) / t));
	} else {
		tmp = t_1 + (x * ((2.0 - ((z - t) / (a - t))) - 1.0));
	}
	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 = ((z / (a - t)) - (t / (a - t))) * y;
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1 + (x * ((z / t) + (((z / Math.pow(t, 2.0)) - (1.0 / t)) * a)));
	} else if (t_2 <= -5e-259) {
		tmp = (((z - t) * y) / (a - t)) - ((((z - t) * x) / (a - t)) - x);
	} else if (t_2 <= 0.0) {
		tmp = t_1 + (x * -((a - z) / t));
	} else {
		tmp = t_1 + (x * ((2.0 - ((z - t) / (a - t))) - 1.0));
	}
	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 = ((z / (a - t)) - (t / (a - t))) * y
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1 + (x * ((z / t) + (((z / math.pow(t, 2.0)) - (1.0 / t)) * a)))
	elif t_2 <= -5e-259:
		tmp = (((z - t) * y) / (a - t)) - ((((z - t) * x) / (a - t)) - x)
	elif t_2 <= 0.0:
		tmp = t_1 + (x * -((a - z) / t))
	else:
		tmp = t_1 + (x * ((2.0 - ((z - t) / (a - t))) - 1.0))
	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(Float64(Float64(z / Float64(a - t)) - Float64(t / Float64(a - t))) * y)
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(t_1 + Float64(x * Float64(Float64(z / t) + Float64(Float64(Float64(z / (t ^ 2.0)) - Float64(1.0 / t)) * a))));
	elseif (t_2 <= -5e-259)
		tmp = Float64(Float64(Float64(Float64(z - t) * y) / Float64(a - t)) - Float64(Float64(Float64(Float64(z - t) * x) / Float64(a - t)) - x));
	elseif (t_2 <= 0.0)
		tmp = Float64(t_1 + Float64(x * Float64(-Float64(Float64(a - z) / t))));
	else
		tmp = Float64(t_1 + Float64(x * Float64(Float64(2.0 - Float64(Float64(z - t) / Float64(a - t))) - 1.0)));
	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 = ((z / (a - t)) - (t / (a - t))) * y;
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1 + (x * ((z / t) + (((z / (t ^ 2.0)) - (1.0 / t)) * a)));
	elseif (t_2 <= -5e-259)
		tmp = (((z - t) * y) / (a - t)) - ((((z - t) * x) / (a - t)) - x);
	elseif (t_2 <= 0.0)
		tmp = t_1 + (x * -((a - z) / t));
	else
		tmp = t_1 + (x * ((2.0 - ((z - t) / (a - t))) - 1.0));
	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[(N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(t$95$1 + N[(x * N[(N[(z / t), $MachinePrecision] + N[(N[(N[(z / N[Power[t, 2.0], $MachinePrecision]), $MachinePrecision] - N[(1.0 / t), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-259], N[(N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(z - t), $MachinePrecision] * x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t$95$1 + N[(x * (-N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x * N[(N[(2.0 - N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	24.7
Target	9.9
Herbie	5.6

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

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 64.0

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

   2. Taylor expanded in y around 0 38.9

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

   3. Taylor expanded in x around 0 11.9

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

   4. Simplified 11.9

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

      [Start] 11.9	\[ \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + \left(1 + -1 \cdot \frac{z - t}{a - t}\right) \cdot x \]
      rational.json-simplify-2 [=>] 11.9	\[ \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
      rational.json-simplify-2 [=>] 11.9	\[ \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + x \cdot \left(1 + \color{blue}{\frac{z - t}{a - t} \cdot -1}\right) \]
      rational.json-simplify-9 [=>] 11.9	\[ \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + x \cdot \left(1 + \color{blue}{\left(-\frac{z - t}{a - t}\right)}\right) \]

   5. Taylor expanded in a around 0 16.0

      \[\leadsto \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + x \cdot \color{blue}{\left(\frac{z}{t} + \left(\frac{z}{{t}^{2}} - \frac{1}{t}\right) \cdot a\right)} \]

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.99999999999999977e-259

   1. Initial program 2.2

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

   2. Taylor expanded in y around -inf 2.2

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

   3. Simplified 2.2

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

      [Start] 2.2	\[ -1 \cdot \frac{\left(z - t\right) \cdot x}{a - t} + \left(\frac{\left(z - t\right) \cdot y}{a - t} + x\right) \]
      rational.json-simplify-2 [=>] 2.2	\[ \color{blue}{\frac{\left(z - t\right) \cdot x}{a - t} \cdot -1} + \left(\frac{\left(z - t\right) \cdot y}{a - t} + x\right) \]
      rational.json-simplify-9 [=>] 2.2	\[ \color{blue}{\left(-\frac{\left(z - t\right) \cdot x}{a - t}\right)} + \left(\frac{\left(z - t\right) \cdot y}{a - t} + x\right) \]
      rational.json-simplify-1 [=>] 2.2	\[ \left(-\frac{\left(z - t\right) \cdot x}{a - t}\right) + \color{blue}{\left(x + \frac{\left(z - t\right) \cdot y}{a - t}\right)} \]

   4. Applied egg-rr 2.0

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

   if -4.99999999999999977e-259 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 56.5

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

   2. Taylor expanded in y around 0 31.7

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

   3. Taylor expanded in x around 0 31.4

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

   4. Simplified 31.4

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

      [Start] 31.4	\[ \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + \left(1 + -1 \cdot \frac{z - t}{a - t}\right) \cdot x \]
      rational.json-simplify-2 [=>] 31.4	\[ \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
      rational.json-simplify-2 [=>] 31.4	\[ \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + x \cdot \left(1 + \color{blue}{\frac{z - t}{a - t} \cdot -1}\right) \]
      rational.json-simplify-9 [=>] 31.4	\[ \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + x \cdot \left(1 + \color{blue}{\left(-\frac{z - t}{a - t}\right)}\right) \]

   5. Taylor expanded in t around -inf 4.1

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

   6. Simplified 4.1

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

      [Start] 4.1	\[ \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + x \cdot \left(-1 \cdot \frac{a - z}{t}\right) \]
      rational.json-simplify-2 [=>] 4.1	\[ \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + x \cdot \color{blue}{\left(\frac{a - z}{t} \cdot -1\right)} \]
      rational.json-simplify-9 [=>] 4.1	\[ \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + x \cdot \color{blue}{\left(-\frac{a - z}{t}\right)} \]

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

   1. Initial program 21.5

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

   2. Taylor expanded in y around 0 14.0

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

   3. Taylor expanded in x around 0 5.2

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

   4. Simplified 5.2

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

      [Start] 5.2	\[ \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + \left(1 + -1 \cdot \frac{z - t}{a - t}\right) \cdot x \]
      rational.json-simplify-2 [=>] 5.2	\[ \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
      rational.json-simplify-2 [=>] 5.2	\[ \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + x \cdot \left(1 + \color{blue}{\frac{z - t}{a - t} \cdot -1}\right) \]
      rational.json-simplify-9 [=>] 5.2	\[ \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + x \cdot \left(1 + \color{blue}{\left(-\frac{z - t}{a - t}\right)}\right) \]

   5. Applied egg-rr 5.2

      \[\leadsto \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + x \cdot \color{blue}{\left(\left(2 - \frac{z - t}{a - t}\right) - 1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 5.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + x \cdot \left(\frac{z}{t} + \left(\frac{z}{{t}^{2}} - \frac{1}{t}\right) \cdot a\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-259}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a - t} - \left(\frac{\left(z - t\right) \cdot x}{a - t} - x\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + x \cdot \left(-\frac{a - z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + x \cdot \left(\left(2 - \frac{z - t}{a - t}\right) - 1\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	6.5
Cost	5008

\[\begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{a - t} - \left(\frac{\left(z - t\right) \cdot x}{a - t} - x\right)\\ t_2 := \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + x \cdot \left(-\frac{a - z}{t}\right)\\ t_3 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-259}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{-299}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+290}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	11.7
Cost	4944

\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ t_2 := \frac{\left(z - t\right) \cdot y}{a - t} - \left(\frac{\left(z - t\right) \cdot x}{a - t} - x\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+306}:\\ \;\;\;\;z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-259}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-299}:\\ \;\;\;\;y + \left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+290}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y\\ \end{array} \]

Alternative 3
Error	12.1
Cost	4432

\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+306}:\\ \;\;\;\;z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-259}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{-262}:\\ \;\;\;\;y + \left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+290}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y\\ \end{array} \]

Alternative 4
Error	12.1
Cost	4432

\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+306}:\\ \;\;\;\;z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-259}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y + \left(z - t\right) \cdot \left(-x\right)}{a - t}\\ \mathbf{elif}\;t_1 \leq 10^{-262}:\\ \;\;\;\;y + \left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+290}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y\\ \end{array} \]

Alternative 5
Error	5.4
Cost	4428

\[\begin{array}{l} t_1 := \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y\\ t_2 := t_1 + x \cdot \left(-\frac{a - z}{t}\right)\\ t_3 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-259}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a - t} - \left(\frac{\left(z - t\right) \cdot x}{a - t} - x\right)\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 + x \cdot \left(\left(2 - \frac{z - t}{a - t}\right) - 1\right)\\ \end{array} \]

Alternative 6
Error	5.4
Cost	4364

\[\begin{array}{l} t_1 := \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y\\ t_2 := t_1 + x \cdot \left(-\frac{a - z}{t}\right)\\ t_3 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-259}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a - t} - \left(\frac{\left(z - t\right) \cdot x}{a - t} - x\right)\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 + x \cdot \left(1 + \left(-\frac{z - t}{a - t}\right)\right)\\ \end{array} \]

Alternative 7
Error	26.9
Cost	2020

\[\begin{array}{l} t_1 := \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y\\ t_2 := x + \frac{\left(z - t\right) \cdot y}{a - t}\\ t_3 := z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)\\ t_4 := x + \frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{if}\;z \leq -1.28 \cdot 10^{+182}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+44}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-232}:\\ \;\;\;\;y + \left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+60}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 8
Error	35.6
Cost	1768

\[\begin{array}{l} t_1 := \left(1 - \frac{z}{a}\right) \cdot x\\ \mathbf{if}\;t \leq -8.4 \cdot 10^{+206}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -0.00031:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-301}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-63}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+107}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+136}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9
Error	35.3
Cost	1768

\[\begin{array}{l} t_1 := \left(1 - \frac{z}{a}\right) \cdot x\\ \mathbf{if}\;t \leq -9.4 \cdot 10^{+206}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+132}:\\ \;\;\;\;x \cdot \left(-\frac{a - z}{t}\right)\\ \mathbf{elif}\;t \leq -0.000345:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-63}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+106}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+136}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 10
Error	33.8
Cost	1768

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a - t}\right)\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+206}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \left(-\frac{a - z}{t}\right)\\ \mathbf{elif}\;t \leq -0.016:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-301}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-63}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{+107}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+136}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 11
Error	30.2
Cost	1764

\[\begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{+206}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -6 \cdot 10^{+136}:\\ \;\;\;\;x \cdot \left(-\frac{a - z}{t}\right)\\ \mathbf{elif}\;t \leq -0.00031:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-91}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a} + x\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-63}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(1 - \frac{z - t}{a - t}\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+130}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+176}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 12
Error	35.3
Cost	1504

\[\begin{array}{l} t_1 := \left(1 - \frac{z}{a}\right) \cdot x\\ \mathbf{if}\;t \leq -8.4 \cdot 10^{+206}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -0.000345:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-63}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 13
Error	30.5
Cost	1504

\[\begin{array}{l} \mathbf{if}\;t \leq -8.4 \cdot 10^{+206}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{+136}:\\ \;\;\;\;x \cdot \left(-\frac{a - z}{t}\right)\\ \mathbf{elif}\;t \leq -0.000345:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-91}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a} + x\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-63}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a - t}\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+107}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+135}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 14
Error	30.4
Cost	1504

\[\begin{array}{l} \mathbf{if}\;t \leq -8.4 \cdot 10^{+206}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(-\frac{a - z}{t}\right)\\ \mathbf{elif}\;t \leq -0.00031:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-91}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a} + x\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-63}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a - t}\right)\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+107}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+130}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 15
Error	27.9
Cost	1504

\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{if}\;t \leq -9.4 \cdot 10^{+206}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \left(-\frac{a - z}{t}\right)\\ \mathbf{elif}\;t \leq -24000:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-63}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+106}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+141}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 16
Error	39.0
Cost	1372

\[\begin{array}{l} t_1 := z \cdot \frac{y - x}{a}\\ \mathbf{if}\;t \leq -8.4 \cdot 10^{+206}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -0.000345:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-182}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-277}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.76 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 17
Error	22.8
Cost	1296

\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot z}{a - t}\\ t_2 := y + \left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)\\ \mathbf{if}\;t \leq -8:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Error	37.1
Cost	1044

\[\begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-193}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-104}:\\ \;\;\;\;\frac{z \cdot x}{t}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-46}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-9}:\\ \;\;\;\;-\frac{z \cdot x}{a}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+36}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19
Error	37.2
Cost	1044

\[\begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-193}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-105}:\\ \;\;\;\;\frac{z \cdot x}{t}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-46}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \left(-\frac{x}{a}\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+33}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20
Error	36.8
Cost	716

\[\begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-192}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-106}:\\ \;\;\;\;\frac{z \cdot x}{t}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+32}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21
Error	37.8
Cost	592

\[\begin{array}{l} \mathbf{if}\;t \leq -8.4 \cdot 10^{+206}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -0.000345:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 22
Error	35.8
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+28}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 23
Error	45.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023077 
(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))))