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

Average Error: 16.2 → 5.2

Time: 14.8s

Precision: binary64

Cost: 3533

Math

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

↓

\[\begin{array}{l} t_1 := \left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \left(z - a\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-175} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z - t}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]

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 (- t z)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (+ x (* (- z a) (/ y t)))
     (if (or (<= t_1 -5e-175) (not (<= t_1 0.0)))
       (+ x (- y (/ y (/ (- a t) (- z t)))))
       (+ x (/ (* y (- z a)) t))))))

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 * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + ((z - a) * (y / t));
	} else if ((t_1 <= -5e-175) || !(t_1 <= 0.0)) {
		tmp = x + (y - (y / ((a - t) / (z - t))));
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	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 * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + ((z - a) * (y / t));
	} else if ((t_1 <= -5e-175) || !(t_1 <= 0.0)) {
		tmp = x + (y - (y / ((a - t) / (z - t))));
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	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 * (t - z)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + ((z - a) * (y / t))
	elif (t_1 <= -5e-175) or not (t_1 <= 0.0):
		tmp = x + (y - (y / ((a - t) / (z - t))))
	else:
		tmp = x + ((y * (z - a)) / t)
	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(Float64(x + y) + Float64(Float64(y * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(z - a) * Float64(y / t)));
	elseif ((t_1 <= -5e-175) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(y - Float64(y / Float64(Float64(a - t) / Float64(z - t)))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	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 * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + ((z - a) * (y / t));
	elseif ((t_1 <= -5e-175) || ~((t_1 <= 0.0)))
		tmp = x + (y - (y / ((a - t) / (z - t))));
	else
		tmp = x + ((y * (z - a)) / t);
	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[(N[(x + y), $MachinePrecision] + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(z - a), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -5e-175], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(y - N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	16.2
Target	8.0
Herbie	5.2

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 64.0

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

   2. Simplified 17.8

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

      [Start] 64.0	\[ \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
      associate--l+ [=>] 64.0	\[ \color{blue}{x + \left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)} \]
      sub-neg [=>] 64.0	\[ x + \color{blue}{\left(y + \left(-\frac{\left(z - t\right) \cdot y}{a - t}\right)\right)} \]
      +-commutative [=>] 64.0	\[ x + \color{blue}{\left(\left(-\frac{\left(z - t\right) \cdot y}{a - t}\right) + y\right)} \]
      neg-mul-1 [=>] 64.0	\[ x + \left(\color{blue}{-1 \cdot \frac{\left(z - t\right) \cdot y}{a - t}} + y\right) \]
      associate-*l/ [<=] 17.9	\[ x + \left(-1 \cdot \color{blue}{\left(\frac{z - t}{a - t} \cdot y\right)} + y\right) \]
      associate-*r* [=>] 17.9	\[ x + \left(\color{blue}{\left(-1 \cdot \frac{z - t}{a - t}\right) \cdot y} + y\right) \]
      fma-def [=>] 17.8	\[ x + \color{blue}{\mathsf{fma}\left(-1 \cdot \frac{z - t}{a - t}, y, y\right)} \]
      mul-1-neg [=>] 17.8	\[ x + \mathsf{fma}\left(\color{blue}{-\frac{z - t}{a - t}}, y, y\right) \]
      neg-sub0 [=>] 17.8	\[ x + \mathsf{fma}\left(\color{blue}{0 - \frac{z - t}{a - t}}, y, y\right) \]
      div-sub [=>] 17.8	\[ x + \mathsf{fma}\left(0 - \color{blue}{\left(\frac{z}{a - t} - \frac{t}{a - t}\right)}, y, y\right) \]
      associate--r- [=>] 17.8	\[ x + \mathsf{fma}\left(\color{blue}{\left(0 - \frac{z}{a - t}\right) + \frac{t}{a - t}}, y, y\right) \]
      neg-sub0 [<=] 17.8	\[ x + \mathsf{fma}\left(\color{blue}{\left(-\frac{z}{a - t}\right)} + \frac{t}{a - t}, y, y\right) \]
      +-commutative [=>] 17.8	\[ x + \mathsf{fma}\left(\color{blue}{\frac{t}{a - t} + \left(-\frac{z}{a - t}\right)}, y, y\right) \]
      sub-neg [<=] 17.8	\[ x + \mathsf{fma}\left(\color{blue}{\frac{t}{a - t} - \frac{z}{a - t}}, y, y\right) \]
      div-sub [<=] 17.8	\[ x + \mathsf{fma}\left(\color{blue}{\frac{t - z}{a - t}}, y, y\right) \]

   3. Taylor expanded in t around inf 58.6

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

   4. Simplified 20.6

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

      [Start] 58.6	\[ y + \left(\frac{y \cdot \left(z - a\right)}{t} + \left(-1 \cdot y + x\right)\right) \]
      +-commutative [=>] 58.6	\[ \color{blue}{\left(\frac{y \cdot \left(z - a\right)}{t} + \left(-1 \cdot y + x\right)\right) + y} \]
      associate-+l+ [=>] 49.0	\[ \color{blue}{\frac{y \cdot \left(z - a\right)}{t} + \left(\left(-1 \cdot y + x\right) + y\right)} \]
      associate-/l* [=>] 31.1	\[ \color{blue}{\frac{y}{\frac{t}{z - a}}} + \left(\left(-1 \cdot y + x\right) + y\right) \]
      associate-/r/ [=>] 29.8	\[ \color{blue}{\frac{y}{t} \cdot \left(z - a\right)} + \left(\left(-1 \cdot y + x\right) + y\right) \]
      +-commutative [<=] 29.8	\[ \frac{y}{t} \cdot \left(z - a\right) + \color{blue}{\left(y + \left(-1 \cdot y + x\right)\right)} \]
      associate-+r+ [=>] 20.6	\[ \frac{y}{t} \cdot \left(z - a\right) + \color{blue}{\left(\left(y + -1 \cdot y\right) + x\right)} \]
      +-commutative [=>] 20.6	\[ \frac{y}{t} \cdot \left(z - a\right) + \color{blue}{\left(x + \left(y + -1 \cdot y\right)\right)} \]
      distribute-rgt1-in [=>] 20.6	\[ \frac{y}{t} \cdot \left(z - a\right) + \left(x + \color{blue}{\left(-1 + 1\right) \cdot y}\right) \]
      metadata-eval [=>] 20.6	\[ \frac{y}{t} \cdot \left(z - a\right) + \left(x + \color{blue}{0} \cdot y\right) \]
      mul0-lft [=>] 20.6	\[ \frac{y}{t} \cdot \left(z - a\right) + \left(x + \color{blue}{0}\right) \]

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -5e-175 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 7.7

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

   2. Simplified 3.7

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

      [Start] 7.7	\[ \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
      +-rgt-identity [<=] 7.7	\[ \color{blue}{\left(\left(x + y\right) + 0\right)} - \frac{\left(z - t\right) \cdot y}{a - t} \]
      associate-+l+ [=>] 7.7	\[ \color{blue}{\left(x + \left(y + 0\right)\right)} - \frac{\left(z - t\right) \cdot y}{a - t} \]
      associate-+r- [<=] 7.5	\[ \color{blue}{x + \left(\left(y + 0\right) - \frac{\left(z - t\right) \cdot y}{a - t}\right)} \]
      +-rgt-identity [=>] 7.5	\[ x + \left(\color{blue}{y} - \frac{\left(z - t\right) \cdot y}{a - t}\right) \]
      *-commutative [=>] 7.5	\[ x + \left(y - \frac{\color{blue}{y \cdot \left(z - t\right)}}{a - t}\right) \]
      associate-/l* [=>] 3.7	\[ x + \left(y - \color{blue}{\frac{y}{\frac{a - t}{z - t}}}\right) \]

   if -5e-175 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 51.3

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

   2. Simplified 52.3

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

      [Start] 51.3	\[ \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
      associate--l+ [=>] 28.7	\[ \color{blue}{x + \left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)} \]
      sub-neg [=>] 28.7	\[ x + \color{blue}{\left(y + \left(-\frac{\left(z - t\right) \cdot y}{a - t}\right)\right)} \]
      +-commutative [=>] 28.7	\[ x + \color{blue}{\left(\left(-\frac{\left(z - t\right) \cdot y}{a - t}\right) + y\right)} \]
      distribute-neg-frac [=>] 28.7	\[ x + \left(\color{blue}{\frac{-\left(z - t\right) \cdot y}{a - t}} + y\right) \]
      distribute-rgt-neg-in [=>] 28.7	\[ x + \left(\frac{\color{blue}{\left(z - t\right) \cdot \left(-y\right)}}{a - t} + y\right) \]
      associate-*r/ [<=] 39.2	\[ x + \left(\color{blue}{\left(z - t\right) \cdot \frac{-y}{a - t}} + y\right) \]
      mul-1-neg [<=] 39.2	\[ x + \left(\left(z - t\right) \cdot \frac{\color{blue}{-1 \cdot y}}{a - t} + y\right) \]
      associate-*r/ [<=] 39.2	\[ x + \left(\left(z - t\right) \cdot \color{blue}{\left(-1 \cdot \frac{y}{a - t}\right)} + y\right) \]
      fma-def [=>] 52.3	\[ x + \color{blue}{\mathsf{fma}\left(z - t, -1 \cdot \frac{y}{a - t}, y\right)} \]

   3. Taylor expanded in t around inf 42.5

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

   4. Simplified 9.1

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

      [Start] 42.5	\[ -1 \cdot \frac{a \cdot y}{t} + \left(y + \left(\frac{y \cdot z}{t} + \left(-1 \cdot y + x\right)\right)\right) \]
      associate-+r+ [=>] 56.4	\[ \color{blue}{\left(-1 \cdot \frac{a \cdot y}{t} + y\right) + \left(\frac{y \cdot z}{t} + \left(-1 \cdot y + x\right)\right)} \]
      associate-+r+ [=>] 56.4	\[ \left(-1 \cdot \frac{a \cdot y}{t} + y\right) + \color{blue}{\left(\left(\frac{y \cdot z}{t} + -1 \cdot y\right) + x\right)} \]
      associate-+r+ [=>] 33.7	\[ \color{blue}{\left(\left(-1 \cdot \frac{a \cdot y}{t} + y\right) + \left(\frac{y \cdot z}{t} + -1 \cdot y\right)\right) + x} \]
      associate-+r+ [<=] 19.3	\[ \color{blue}{\left(-1 \cdot \frac{a \cdot y}{t} + \left(y + \left(\frac{y \cdot z}{t} + -1 \cdot y\right)\right)\right)} + x \]
      +-commutative [=>] 19.3	\[ \color{blue}{\left(\left(y + \left(\frac{y \cdot z}{t} + -1 \cdot y\right)\right) + -1 \cdot \frac{a \cdot y}{t}\right)} + x \]
      mul-1-neg [=>] 19.3	\[ \left(\left(y + \left(\frac{y \cdot z}{t} + -1 \cdot y\right)\right) + \color{blue}{\left(-\frac{a \cdot y}{t}\right)}\right) + x \]
      unsub-neg [=>] 19.3	\[ \color{blue}{\left(\left(y + \left(\frac{y \cdot z}{t} + -1 \cdot y\right)\right) - \frac{a \cdot y}{t}\right)} + x \]
      +-commutative [=>] 19.3	\[ \left(\color{blue}{\left(\left(\frac{y \cdot z}{t} + -1 \cdot y\right) + y\right)} - \frac{a \cdot y}{t}\right) + x \]
      associate-+l+ [=>] 5.7	\[ \left(\color{blue}{\left(\frac{y \cdot z}{t} + \left(-1 \cdot y + y\right)\right)} - \frac{a \cdot y}{t}\right) + x \]
      associate-/l* [=>] 5.6	\[ \left(\left(\color{blue}{\frac{y}{\frac{t}{z}}} + \left(-1 \cdot y + y\right)\right) - \frac{a \cdot y}{t}\right) + x \]
      associate-/r/ [=>] 9.0	\[ \left(\left(\color{blue}{\frac{y}{t} \cdot z} + \left(-1 \cdot y + y\right)\right) - \frac{a \cdot y}{t}\right) + x \]
      distribute-lft1-in [=>] 9.0	\[ \left(\left(\frac{y}{t} \cdot z + \color{blue}{\left(-1 + 1\right) \cdot y}\right) - \frac{a \cdot y}{t}\right) + x \]
      metadata-eval [=>] 9.0	\[ \left(\left(\frac{y}{t} \cdot z + \color{blue}{0} \cdot y\right) - \frac{a \cdot y}{t}\right) + x \]
      mul0-lft [=>] 9.0	\[ \left(\left(\frac{y}{t} \cdot z + \color{blue}{0}\right) - \frac{a \cdot y}{t}\right) + x \]
      associate-/l* [=>] 9.8	\[ \left(\left(\frac{y}{t} \cdot z + 0\right) - \color{blue}{\frac{a}{\frac{t}{y}}}\right) + x \]
      associate-/r/ [=>] 9.1	\[ \left(\left(\frac{y}{t} \cdot z + 0\right) - \color{blue}{\frac{a}{t} \cdot y}\right) + x \]

   5. Taylor expanded in t around 0 5.7

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

   6. Simplified 5.7

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

      [Start] 5.7	\[ \frac{y \cdot z - a \cdot y}{t} + x \]
      *-commutative [=>] 5.7	\[ \frac{y \cdot z - \color{blue}{y \cdot a}}{t} + x \]
      distribute-lft-out-- [=>] 5.7	\[ \frac{\color{blue}{y \cdot \left(z - a\right)}}{t} + x \]

3. Recombined 3 regimes into one program.

4. Final simplification 5.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \left(z - a\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -5 \cdot 10^{-175} \lor \neg \left(\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z - t}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]

Alternatives

Alternative 1
Error	3.8
Cost	8260

\[\begin{array}{l} t_1 := \left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-286}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}, x\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z - t}}\right)\\ \end{array} \]

Alternative 2
Error	12.4
Cost	972

\[\begin{array}{l} t_1 := x + \left(z - a\right) \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-136}:\\ \;\;\;\;\left(x + y\right) - \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{+140}:\\ \;\;\;\;x + \frac{y \cdot z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	8.0
Cost	969

\[\begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+128} \lor \neg \left(t \leq 8.8 \cdot 10^{+14}\right):\\ \;\;\;\;x + \left(z - a\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{z}{\frac{a - t}{y}}\\ \end{array} \]

Alternative 4
Error	9.5
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+21} \lor \neg \left(a \leq 1.15 \cdot 10^{+111}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t - a}\\ \end{array} \]

Alternative 5
Error	11.4
Cost	840

\[\begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+62}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+112}:\\ \;\;\;\;x + \frac{y \cdot z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Error	9.7
Cost	840

\[\begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+21}:\\ \;\;\;\;\left(x + y\right) - \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+111}:\\ \;\;\;\;x + \frac{y \cdot z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 7
Error	20.1
Cost	720

\[\begin{array}{l} \mathbf{if}\;a \leq -2300000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-288}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{-259}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8
Error	15.4
Cost	713

\[\begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+21} \lor \neg \left(a \leq 6.5 \cdot 10^{-123}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]

Alternative 9
Error	27.1
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -2.85 \cdot 10^{-199}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-308}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-266}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.96 \cdot 10^{-150}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Error	19.8
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -82000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-95}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11
Error	28.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023039 
(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))))