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

Average Error: 24.7 → 7.3

Time: 17.6s

Precision: binary64

Cost: 4496

Math

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

↓

\[\begin{array}{l} t_1 := t + \left(\frac{a}{z} - \frac{y}{z}\right) \cdot \left(t + \left(-x\right)\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-287}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+299}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 (+ t (* (- (/ a z) (/ y z)) (+ t (- x)))))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-287)
       t_2
       (if (<= t_2 0.0) t_1 (if (<= t_2 2e+299) t_2 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 = t + (((a / z) - (y / z)) * (t + -x));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-287) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 2e+299) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

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

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((a / z) - (y / z)) * (t + -x));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-287) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 2e+299) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	t_1 = t + (((a / z) - (y / z)) * (t + -x))
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-287:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t_1
	elif t_2 <= 2e+299:
		tmp = t_2
	else:
		tmp = 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(t + Float64(Float64(Float64(a / z) - Float64(y / z)) * Float64(t + Float64(-x))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-287)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 2e+299)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((a / z) - (y / z)) * (t + -x));
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-287)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 2e+299)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = 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[(t + N[(N[(N[(a / z), $MachinePrecision] - N[(y / z), $MachinePrecision]), $MachinePrecision] * N[(t + (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-287], t$95$2, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 2e+299], t$95$2, t$95$1]]]]]]

Target

Original	24.7
Target	12.2
Herbie	7.3

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or -2.00000000000000004e-287 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0 or 2.0000000000000001e299 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 62.4

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

   2. Taylor expanded in z around -inf 31.3

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

   3. Simplified 31.3

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

      [Start] 31.3	\[ -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z} + t \]
      rational_best_oopsla_all_46_json_45_simplify-35 [=>] 31.3	\[ \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 31.3	\[ t + \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z} \cdot -1} \]
      rational_best_oopsla_all_46_json_45_simplify-92 [=>] 31.3	\[ t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 31.3	\[ t + \left(-\frac{y \cdot \left(t - x\right) - \color{blue}{\left(t - x\right) \cdot a}}{z}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-102 [=>] 31.3	\[ t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

   4. Taylor expanded in x around -inf 25.2

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

   5. Simplified 25.2

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

      [Start] 25.2	\[ \left(t + -1 \cdot \left(\left(\frac{a}{z} - \frac{y}{z}\right) \cdot x\right)\right) - \frac{t \cdot \left(y - a\right)}{z} \]
      rational_best_oopsla_all_46_json_45_simplify-35 [=>] 25.2	\[ \color{blue}{\left(-1 \cdot \left(\left(\frac{a}{z} - \frac{y}{z}\right) \cdot x\right) + t\right)} - \frac{t \cdot \left(y - a\right)}{z} \]
      rational_best_oopsla_all_46_json_45_simplify-107 [=>] 25.2	\[ \color{blue}{t + \left(-1 \cdot \left(\left(\frac{a}{z} - \frac{y}{z}\right) \cdot x\right) - \frac{t \cdot \left(y - a\right)}{z}\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-7 [=>] 25.2	\[ t + \left(\color{blue}{\left(\frac{a}{z} - \frac{y}{z}\right) \cdot \left(-1 \cdot x\right)} - \frac{t \cdot \left(y - a\right)}{z}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 25.2	\[ t + \left(\left(\frac{a}{z} - \frac{y}{z}\right) \cdot \color{blue}{\left(x \cdot -1\right)} - \frac{t \cdot \left(y - a\right)}{z}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-94 [<=] 25.2	\[ t + \left(\left(\frac{a}{z} - \frac{y}{z}\right) \cdot \color{blue}{\left(-x\right)} - \frac{t \cdot \left(y - a\right)}{z}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 25.2	\[ t + \left(\left(\frac{a}{z} - \frac{y}{z}\right) \cdot \left(-x\right) - \frac{\color{blue}{\left(y - a\right) \cdot t}}{z}\right) \]

   6. Taylor expanded in t around 0 16.1

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

   7. Simplified 16.1

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

      [Start] 16.1	\[ t + \left(\left(\frac{a}{z} - \frac{y}{z}\right) \cdot t + -1 \cdot \left(\left(\frac{a}{z} - \frac{y}{z}\right) \cdot x\right)\right) \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 16.1	\[ t + \left(\color{blue}{t \cdot \left(\frac{a}{z} - \frac{y}{z}\right)} + -1 \cdot \left(\left(\frac{a}{z} - \frac{y}{z}\right) \cdot x\right)\right) \]
      rational_best_oopsla_all_46_json_45_simplify-7 [=>] 16.1	\[ t + \left(t \cdot \left(\frac{a}{z} - \frac{y}{z}\right) + \color{blue}{\left(\frac{a}{z} - \frac{y}{z}\right) \cdot \left(-1 \cdot x\right)}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-23 [=>] 16.1	\[ t + \color{blue}{\left(\frac{a}{z} - \frac{y}{z}\right) \cdot \left(t + -1 \cdot x\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [<=] 16.1	\[ t + \left(\frac{a}{z} - \frac{y}{z}\right) \cdot \left(t + \color{blue}{x \cdot -1}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-94 [<=] 16.1	\[ t + \left(\frac{a}{z} - \frac{y}{z}\right) \cdot \left(t + \color{blue}{\left(-x\right)}\right) \]

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -2.00000000000000004e-287 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 2.0000000000000001e299

   1. Initial program 1.9

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

4. Final simplification 7.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -\infty:\\ \;\;\;\;t + \left(\frac{a}{z} - \frac{y}{z}\right) \cdot \left(t + \left(-x\right)\right)\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -2 \cdot 10^{-287}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + \left(\frac{a}{z} - \frac{y}{z}\right) \cdot \left(t + \left(-x\right)\right)\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 2 \cdot 10^{+299}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \left(\frac{a}{z} - \frac{y}{z}\right) \cdot \left(t + \left(-x\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	8.8
Cost	4432

\[\begin{array}{l} t_1 := t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-287}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right)\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+299}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	35.1
Cost	2032

\[\begin{array}{l} t_1 := t \cdot \left(-\frac{z}{a - z}\right)\\ t_2 := x - x \cdot \frac{y}{a}\\ t_3 := t - \frac{y \cdot t}{z}\\ \mathbf{if}\;a \leq -3 \cdot 10^{+137}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-36}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-268}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-148}:\\ \;\;\;\;-\frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-92}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+123}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+232}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	40.4
Cost	1832

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ t_2 := -\frac{y \cdot \left(t - x\right)}{z}\\ t_3 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+165}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+99}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{+72}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-83}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-101}:\\ \;\;\;\;\frac{\left(y - a\right) \cdot x}{z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+66}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+210}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 4
Error	32.9
Cost	1504

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -4.3 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-35}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-92}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+18}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+102}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	36.3
Cost	1240

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+111}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -16:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-301}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.16 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-11}:\\ \;\;\;\;\frac{z \cdot x}{a} + x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6
Error	34.5
Cost	1240

\[\begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+135}:\\ \;\;\;\;\frac{z \cdot x}{a} + x\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-22}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-92}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+18}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+104}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	19.3
Cost	1232

\[\begin{array}{l} t_1 := x + \frac{t \cdot \left(y - z\right)}{a - z}\\ t_2 := t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-245}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a} + x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	18.9
Cost	1232

\[\begin{array}{l} t_1 := x + \frac{t \cdot \left(y - z\right)}{a - z}\\ t_2 := t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-231}:\\ \;\;\;\;x + \frac{\left(t - x\right) \cdot y}{a - z}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	36.2
Cost	1108

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+110}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -16:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-300}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10
Error	31.3
Cost	1104

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{y}{a - z} - -1\right)\\ \end{array} \]

Alternative 11
Error	23.2
Cost	1100

\[\begin{array}{l} t_1 := t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-110}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a} + x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-53}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a} + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	31.6
Cost	1040

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{if}\;z \leq -18000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(-\frac{y}{z}\right) + 1\right)\\ \end{array} \]

Alternative 13
Error	27.0
Cost	972

\[\begin{array}{l} t_1 := t \cdot \left(\frac{y}{a - z} - -1\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-117}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a} + x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-11}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a} + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	27.9
Cost	840

\[\begin{array}{l} t_1 := t \cdot \left(\frac{y}{a - z} - -1\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-11}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a} + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	35.7
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+40}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-301}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-285}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16
Error	35.5
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+41}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17
Error	45.5
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023090 
(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))))