Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B

Average Error: 16.0 → 4.9

Time: 15.8s

Precision: binary64

Cost: 4432

Math

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

↓

\[\begin{array}{l} t_1 := x + \left(y - \frac{y}{\frac{a - t}{z - t}}\right)\\ t_2 := \left(y + x\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - a\right) + x\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+242}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- y (/ y (/ (- a t) (- z t))))))
        (t_2 (+ (+ y x) (/ (* y (- t z)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-255)
       t_2
       (if (<= t_2 0.0)
         (+ (* (/ y t) (- z a)) x)
         (if (<= t_2 2e+242) t_2 t_1))))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y - (y / ((a - t) / (z - t))));
	double t_2 = (y + x) + ((y * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-255) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = ((y / t) * (z - a)) + x;
	} else if (t_2 <= 2e+242) {
		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) * y) / (a - t));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y - (y / ((a - t) / (z - t))));
	double t_2 = (y + x) + ((y * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-255) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = ((y / t) * (z - a)) + x;
	} else if (t_2 <= 2e+242) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	t_1 = x + (y - (y / ((a - t) / (z - t))))
	t_2 = (y + x) + ((y * (t - z)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-255:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = ((y / t) * (z - a)) + x
	elif t_2 <= 2e+242:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

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

↓

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y - Float64(y / Float64(Float64(a - t) / Float64(z - t)))))
	t_2 = Float64(Float64(y + x) + Float64(Float64(y * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-255)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(y / t) * Float64(z - a)) + x);
	elseif (t_2 <= 2e+242)
		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) * y) / (a - t));
end

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y - (y / ((a - t) / (z - t))));
	t_2 = (y + x) + ((y * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-255)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = ((y / t) * (z - a)) + x;
	elseif (t_2 <= 2e+242)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y - N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y + x), $MachinePrecision] + N[(N[(y * 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, -2e-255], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 2e+242], t$95$2, t$95$1]]]]]]

Target

Original	16.0
Target	8.4
Herbie	4.9

\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -inf.0 or 2.0000000000000001e242 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 45.8

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

   2. Simplified 15.2

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

      [Start] 45.8	\[ \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
      +-rgt-identity [<=] 45.8	\[ \color{blue}{\left(\left(x + y\right) + 0\right)} - \frac{\left(z - t\right) \cdot y}{a - t} \]
      associate-+l+ [=>] 45.8	\[ \color{blue}{\left(x + \left(y + 0\right)\right)} - \frac{\left(z - t\right) \cdot y}{a - t} \]
      associate-+r- [<=] 45.8	\[ \color{blue}{x + \left(\left(y + 0\right) - \frac{\left(z - t\right) \cdot y}{a - t}\right)} \]
      +-rgt-identity [=>] 45.8	\[ x + \left(\color{blue}{y} - \frac{\left(z - t\right) \cdot y}{a - t}\right) \]
      *-commutative [=>] 45.8	\[ x + \left(y - \frac{\color{blue}{y \cdot \left(z - t\right)}}{a - t}\right) \]
      associate-/l* [=>] 15.2	\[ x + \left(y - \color{blue}{\frac{y}{\frac{a - t}{z - t}}}\right) \]

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -2e-255 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 2.0000000000000001e242

   1. Initial program 1.5

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

   if -2e-255 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 60.0

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

   2. Simplified 35.0

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

      [Start] 60.0	\[ \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
      associate--l+ [=>] 35.1	\[ \color{blue}{x + \left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)} \]
      sub-neg [=>] 35.1	\[ x + \color{blue}{\left(y + \left(-\frac{\left(z - t\right) \cdot y}{a - t}\right)\right)} \]
      +-commutative [=>] 35.1	\[ x + \color{blue}{\left(\left(-\frac{\left(z - t\right) \cdot y}{a - t}\right) + y\right)} \]
      neg-mul-1 [=>] 35.1	\[ x + \left(\color{blue}{-1 \cdot \frac{\left(z - t\right) \cdot y}{a - t}} + y\right) \]
      associate-*l/ [<=] 35.0	\[ x + \left(-1 \cdot \color{blue}{\left(\frac{z - t}{a - t} \cdot y\right)} + y\right) \]
      associate-*r* [=>] 35.0	\[ x + \left(\color{blue}{\left(-1 \cdot \frac{z - t}{a - t}\right) \cdot y} + y\right) \]
      fma-def [=>] 35.0	\[ x + \color{blue}{\mathsf{fma}\left(-1 \cdot \frac{z - t}{a - t}, y, y\right)} \]
      mul-1-neg [=>] 35.0	\[ x + \mathsf{fma}\left(\color{blue}{-\frac{z - t}{a - t}}, y, y\right) \]
      neg-sub0 [=>] 35.0	\[ x + \mathsf{fma}\left(\color{blue}{0 - \frac{z - t}{a - t}}, y, y\right) \]
      div-sub [=>] 35.0	\[ x + \mathsf{fma}\left(0 - \color{blue}{\left(\frac{z}{a - t} - \frac{t}{a - t}\right)}, y, y\right) \]
      associate--r- [=>] 35.0	\[ x + \mathsf{fma}\left(\color{blue}{\left(0 - \frac{z}{a - t}\right) + \frac{t}{a - t}}, y, y\right) \]
      neg-sub0 [<=] 35.0	\[ x + \mathsf{fma}\left(\color{blue}{\left(-\frac{z}{a - t}\right)} + \frac{t}{a - t}, y, y\right) \]
      +-commutative [=>] 35.0	\[ x + \mathsf{fma}\left(\color{blue}{\frac{t}{a - t} + \left(-\frac{z}{a - t}\right)}, y, y\right) \]
      sub-neg [<=] 35.0	\[ x + \mathsf{fma}\left(\color{blue}{\frac{t}{a - t} - \frac{z}{a - t}}, y, y\right) \]
      div-sub [<=] 35.0	\[ x + \mathsf{fma}\left(\color{blue}{\frac{t - z}{a - t}}, y, y\right) \]

   3. Taylor expanded in t around inf 60.6

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

   4. Simplified 6.0

      \[\leadsto \color{blue}{\frac{y}{t} \cdot \left(z - a\right) + \left(x + 0\right)} \]
      Proof

      [Start] 60.6	\[ y + \left(\frac{y \cdot \left(z - a\right)}{t} + \left(-1 \cdot y + x\right)\right) \]
      +-commutative [=>] 60.6	\[ \color{blue}{\left(\frac{y \cdot \left(z - a\right)}{t} + \left(-1 \cdot y + x\right)\right) + y} \]
      associate-+l+ [=>] 28.1	\[ \color{blue}{\frac{y \cdot \left(z - a\right)}{t} + \left(\left(-1 \cdot y + x\right) + y\right)} \]
      associate-/l* [=>] 27.8	\[ \color{blue}{\frac{y}{\frac{t}{z - a}}} + \left(\left(-1 \cdot y + x\right) + y\right) \]
      associate-/r/ [=>] 32.3	\[ \color{blue}{\frac{y}{t} \cdot \left(z - a\right)} + \left(\left(-1 \cdot y + x\right) + y\right) \]
      +-commutative [<=] 32.3	\[ \frac{y}{t} \cdot \left(z - a\right) + \color{blue}{\left(y + \left(-1 \cdot y + x\right)\right)} \]
      associate-+r+ [=>] 6.0	\[ \frac{y}{t} \cdot \left(z - a\right) + \color{blue}{\left(\left(y + -1 \cdot y\right) + x\right)} \]
      +-commutative [=>] 6.0	\[ \frac{y}{t} \cdot \left(z - a\right) + \color{blue}{\left(x + \left(y + -1 \cdot y\right)\right)} \]
      distribute-rgt1-in [=>] 6.0	\[ \frac{y}{t} \cdot \left(z - a\right) + \left(x + \color{blue}{\left(-1 + 1\right) \cdot y}\right) \]
      metadata-eval [=>] 6.0	\[ \frac{y}{t} \cdot \left(z - a\right) + \left(x + \color{blue}{0} \cdot y\right) \]
      mul0-lft [=>] 6.0	\[ \frac{y}{t} \cdot \left(z - a\right) + \left(x + \color{blue}{0}\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 4.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y + x\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z - t}}\right)\\ \mathbf{elif}\;\left(y + x\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{-255}:\\ \;\;\;\;\left(y + x\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;\left(y + x\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - a\right) + x\\ \mathbf{elif}\;\left(y + x\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 2 \cdot 10^{+242}:\\ \;\;\;\;\left(y + x\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z - t}}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	7.1
Cost	7368

\[\begin{array}{l} t_1 := \frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+93}:\\ \;\;\;\;t_1 + \left(t_1 \cdot \frac{a}{t} + x\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+58}:\\ \;\;\;\;x + \mathsf{fma}\left(z - t, \frac{y}{t - a}, y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + x\\ \end{array} \]

Alternative 2
Error	6.4
Cost	3532

\[\begin{array}{l} t_1 := \left(y + x\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-255}:\\ \;\;\;\;\left(y + x\right) + \frac{t - z}{\frac{a - t}{y}}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - a\right) + x\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+242}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z - t}}\right)\\ \end{array} \]

Alternative 3
Error	7.1
Cost	1476

\[\begin{array}{l} t_1 := \frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+93}:\\ \;\;\;\;t_1 + \left(t_1 \cdot \frac{a}{t} + x\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+58}:\\ \;\;\;\;\left(y + x\right) + \frac{t - z}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1 + x\\ \end{array} \]

Alternative 4
Error	12.4
Cost	1368

\[\begin{array}{l} t_1 := \left(y + x\right) - \frac{y}{\frac{a}{z}}\\ t_2 := \frac{y}{t} \cdot \left(z - a\right) + x\\ \mathbf{if}\;t \leq -9 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{y \cdot z}{t - a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-89}:\\ \;\;\;\;\left(y + x\right) - \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \left(1 + \frac{t - z}{a - t}\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	11.8
Cost	1104

\[\begin{array}{l} t_1 := \frac{y}{t} \cdot \left(z - a\right) + x\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-55}:\\ \;\;\;\;\left(y + x\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{y \cdot z}{t - a}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+48}:\\ \;\;\;\;\left(y + x\right) - \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	7.1
Cost	1097

\[\begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{-48} \lor \neg \left(a \leq 1.5 \cdot 10^{-134}\right):\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z - t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - a\right) + x\\ \end{array} \]

Alternative 7
Error	16.2
Cost	1040

\[\begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-23}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-109}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+71}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+114}:\\ \;\;\;\;z \cdot \frac{-y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 8
Error	17.5
Cost	1040

\[\begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-24}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-109}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+71}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{-z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 9
Error	21.8
Cost	848

\[\begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{-189}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.24 \cdot 10^{-194}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 10
Error	21.9
Cost	848

\[\begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{-189}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-229}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-194}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-157}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 11
Error	8.6
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+59} \lor \neg \left(a \leq 1.5 \cdot 10^{-22}\right):\\ \;\;\;\;\left(y + x\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t - a}{z}}\\ \end{array} \]

Alternative 12
Error	10.7
Cost	840

\[\begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+113}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+155}:\\ \;\;\;\;x + \frac{y}{\frac{t - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 13
Error	14.8
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-22}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-109}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 14
Error	20.1
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-14}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 3.45 \cdot 10^{-183}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 15
Error	26.9
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-258}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-87}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Error	28.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023018 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-7) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

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