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

Average Accuracy: 83.2% → 99.6%

Time: 11.7s

Precision: binary64

Cost: 1993

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+306)))
     (+ x (/ (- y z) (/ (- a z) t)))
     (+ t_1 x))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+306)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Java

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

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+306)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+306):
		tmp = x + ((y - z) / ((a - z) / t))
	else:
		tmp = t_1 + x
	return tmp

Julia

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

↓

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+306))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+306)))
		tmp = x + ((y - z) / ((a - z) / t));
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+306]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Target

Original	83.2%
Target	99.1%
Herbie	99.6%

\[\begin{array}{l} \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0 or 4.99999999999999993e306 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 0.2%

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

   2. Simplified 99.7%

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

      [Start] 0.2	\[ x + \frac{\left(y - z\right) \cdot t}{a - z} \]
      associate-/l* [=>] 99.7	\[ x + \color{blue}{\frac{y - z}{\frac{a - z}{t}}} \]

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 4.99999999999999993e306

   1. Initial program 99.6%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 5 \cdot 10^{+306}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	99.1%
Cost	1993

\[\begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+218} \lor \neg \left(t_1 \leq 10^{+260}\right):\\ \;\;\;\;x - t \cdot \frac{z - y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1 + x\\ \end{array} \]

Alternative 2
Accuracy	79.4%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-27} \lor \neg \left(z \leq 3 \cdot 10^{+32}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \end{array} \]

Alternative 3
Accuracy	81.6%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-27} \lor \neg \left(z \leq 8 \cdot 10^{+32}\right):\\ \;\;\;\;x + \frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \end{array} \]

Alternative 4
Accuracy	84.2%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-149} \lor \neg \left(z \leq 9.5 \cdot 10^{-111}\right):\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \end{array} \]

Alternative 5
Accuracy	77.7%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-26} \lor \neg \left(z \leq 9 \cdot 10^{+31}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 6
Accuracy	77.7%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-28} \lor \neg \left(z \leq 1.42 \cdot 10^{+32}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 7
Accuracy	97.9%
Cost	704

\[x - t \cdot \frac{z - y}{a - z} \]

Alternative 8
Accuracy	68.2%
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+162}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Accuracy	54.7%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023136 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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