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

Average Error: 24.1 → 6.5

Time: 32.0s

Precision: binary64

Cost: 4432

Math

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

↓

\[\begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ t_2 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-259}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{+250}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 (* (- z t) (/ (- y x) (- a t)))))
        (t_2 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e-259)
       t_2
       (if (<= t_2 0.0)
         (+ y (/ (* x (- z a)) t))
         (if (<= t_2 4e+250) t_2 t_1))))))

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 + ((z - t) * ((y - x) / (a - t)));
	double t_2 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e-259) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + ((x * (z - a)) / t);
	} else if (t_2 <= 4e+250) {
		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 - x) * (z - t)) / (a - t));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / (a - t)));
	double t_2 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e-259) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + ((x * (z - a)) / t);
	} else if (t_2 <= 4e+250) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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 + ((z - t) * ((y - x) / (a - t)))
	t_2 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e-259:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + ((x * (z - a)) / t)
	elif t_2 <= 4e+250:
		tmp = t_2
	else:
		tmp = t_1
	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(z - t) * Float64(Float64(y - x) / Float64(a - t))))
	t_2 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e-259)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(x * Float64(z - a)) / t));
	elseif (t_2 <= 4e+250)
		tmp = t_2;
	else
		tmp = t_1;
	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 + ((z - t) * ((y - x) / (a - t)));
	t_2 = x - (((y - x) * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e-259)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + ((x * (z - a)) / t);
	elseif (t_2 <= 4e+250)
		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 - 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[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e-259], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+250], t$95$2, t$95$1]]]]]]

Target

Original	24.1
Target	8.7
Herbie	6.5

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

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 3.9999999999999997e250 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 58.2

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

   2. Simplified 15.7

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
      Proof
      (+.f64 x (*.f64 (/.f64 (-.f64 y x) (-.f64 a t)) (-.f64 z t))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))): 0 points increase in error, 0 points decrease in error

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.99999999999999977e-259 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 3.9999999999999997e250

   1. Initial program 2.0

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

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

   1. Initial program 56.9

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

   2. Simplified 56.7

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]
      Proof
      (+.f64 x (*.f64 (/.f64 (-.f64 y x) (-.f64 a t)) (-.f64 z t))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in t around inf 4.4

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

   4. Simplified 4.4

      \[\leadsto \color{blue}{y + \frac{\left(x - y\right) \cdot \left(z - a\right)}{t}} \]
      Proof
      (+.f64 y (/.f64 (*.f64 (-.f64 x y) (-.f64 z a)) t)): 0 points increase in error, 0 points decrease in error
      (+.f64 y (/.f64 (*.f64 (Rewrite<= unsub-neg_binary64 (+.f64 x (neg.f64 y))) (-.f64 z a)) t)): 0 points increase in error, 0 points decrease in error
      (+.f64 y (/.f64 (*.f64 (Rewrite=> +-commutative_binary64 (+.f64 (neg.f64 y) x)) (-.f64 z a)) t)): 0 points increase in error, 17 points decrease in error
      (+.f64 y (/.f64 (*.f64 (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 y)) x) (-.f64 z a)) t)): 17 points increase in error, 0 points decrease in error
      (+.f64 y (/.f64 (*.f64 (Rewrite=> associate-+l-_binary64 (-.f64 0 (-.f64 y x))) (-.f64 z a)) t)): 0 points increase in error, 17 points decrease in error
      (+.f64 y (/.f64 (*.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 y x))) (-.f64 z a)) t)): 17 points increase in error, 0 points decrease in error
      (+.f64 y (/.f64 (*.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (-.f64 y x))) (-.f64 z a)) t)): 0 points increase in error, 17 points decrease in error
      (+.f64 y (/.f64 (Rewrite<= associate-*r*_binary64 (*.f64 -1 (*.f64 (-.f64 y x) (-.f64 z a)))) t)): 17 points increase in error, 0 points decrease in error
      (+.f64 y (/.f64 (*.f64 -1 (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 z (-.f64 y x)) (*.f64 a (-.f64 y x))))) t)): 0 points increase in error, 17 points decrease in error
      (+.f64 y (/.f64 (*.f64 -1 (-.f64 (Rewrite=> *-commutative_binary64 (*.f64 (-.f64 y x) z)) (*.f64 a (-.f64 y x)))) t)): 0 points increase in error, 0 points decrease in error
      (+.f64 y (/.f64 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 -1 (*.f64 (-.f64 y x) z)) (*.f64 -1 (*.f64 a (-.f64 y x))))) t)): 17 points increase in error, 0 points decrease in error
      (+.f64 y (Rewrite=> div-sub_binary64 (-.f64 (/.f64 (*.f64 -1 (*.f64 (-.f64 y x) z)) t) (/.f64 (*.f64 -1 (*.f64 a (-.f64 y x))) t)))): 0 points increase in error, 17 points decrease in error
      (+.f64 y (-.f64 (Rewrite<= associate-*r/_binary64 (*.f64 -1 (/.f64 (*.f64 (-.f64 y x) z) t))) (/.f64 (*.f64 -1 (*.f64 a (-.f64 y x))) t))): 17 points increase in error, 0 points decrease in error
      (+.f64 y (-.f64 (*.f64 -1 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 z (-.f64 y x))) t)) (/.f64 (*.f64 -1 (*.f64 a (-.f64 y x))) t))): 0 points increase in error, 0 points decrease in error
      (+.f64 y (-.f64 (*.f64 -1 (/.f64 (*.f64 z (-.f64 y x)) t)) (Rewrite<= associate-*r/_binary64 (*.f64 -1 (/.f64 (*.f64 a (-.f64 y x)) t))))): 0 points increase in error, 17 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 y (*.f64 -1 (/.f64 (*.f64 z (-.f64 y x)) t))) (*.f64 -1 (/.f64 (*.f64 a (-.f64 y x)) t)))): 17 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (*.f64 z (-.f64 y x)) t)) y)) (*.f64 -1 (/.f64 (*.f64 a (-.f64 y x)) t))): 0 points increase in error, 17 points decrease in error

   5. Taylor expanded in x around inf 4.4

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

4. Final simplification 6.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -5 \cdot 10^{-259}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 4 \cdot 10^{+250}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternatives

Alternative 1
Error	6.6
Cost	2633

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

Alternative 2
Error	42.7
Cost	1636

\[\begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{if}\;x \leq -9 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.28 \cdot 10^{-70}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-296}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-202}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-137}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-59}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	28.9
Cost	1568

\[\begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ t_2 := y + z \cdot \frac{x}{t}\\ \mathbf{if}\;x \leq -5.9 \cdot 10^{+257}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+220}:\\ \;\;\;\;\frac{-x}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 4
Error	21.0
Cost	1496

\[\begin{array}{l} t_1 := y + \left(z - a\right) \cdot \frac{x}{t}\\ t_2 := x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+126}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-6}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot \frac{1}{a - t}\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 5
Error	20.6
Cost	1496

\[\begin{array}{l} t_1 := \frac{a}{z - t}\\ t_2 := y + \left(z - a\right) \cdot \frac{x}{t}\\ t_3 := x + \frac{y - x}{t_1}\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+126}:\\ \;\;\;\;x + \frac{y}{t_1}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{-80}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-6}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot \frac{1}{a - t}\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+113}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 6
Error	20.0
Cost	1496

\[\begin{array}{l} t_1 := x + \frac{t}{a - t} \cdot \left(x - y\right)\\ t_2 := y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-12}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot \frac{1}{a - t}\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 7
Error	20.1
Cost	1496

\[\begin{array}{l} t_1 := x + \frac{t}{a - t} \cdot \left(x - y\right)\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+141}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-29}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-10}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot \frac{1}{a - t}\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 8
Error	27.5
Cost	1240

\[\begin{array}{l} t_1 := y + z \cdot \frac{x}{t}\\ t_2 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3600000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+26}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+164}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+207}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 9
Error	27.5
Cost	1240

\[\begin{array}{l} t_1 := y + z \cdot \frac{x}{t}\\ t_2 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.56 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3800000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+27}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+166}:\\ \;\;\;\;\frac{y}{\frac{a - t}{-t}}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+207}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 10
Error	25.6
Cost	1236

\[\begin{array}{l} t_1 := z \cdot \frac{y - x}{a - t}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -7.1 \cdot 10^{+81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-29}:\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-80}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 22000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	25.5
Cost	1236

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1.18 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-26}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-30}:\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-81}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 120000:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	23.5
Cost	1236

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-273}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-250}:\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{+164}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	23.3
Cost	1236

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+49}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-273}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-250}:\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+164}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 14
Error	21.6
Cost	1236

\[\begin{array}{l} t_1 := y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+126}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 35000:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 15
Error	9.8
Cost	1096

\[\begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+192}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{+162}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]

Alternative 16
Error	22.4
Cost	972

\[\begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+55}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 65000:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 17
Error	36.5
Cost	844

\[\begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+143}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-229}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-294}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 18
Error	27.1
Cost	776

\[\begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-29}:\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 0.28:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \end{array} \]

Alternative 19
Error	26.7
Cost	713

\[\begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-29} \lor \neg \left(t \leq 7 \cdot 10^{-81}\right):\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 20
Error	30.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+145}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+114}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 21
Error	26.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-30}:\\ \;\;\;\;y + \frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-80}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \]

Alternative 22
Error	36.3
Cost	328

\[\begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+143}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 23
Error	45.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022343 
(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))))