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

Average Error: 16.98% → 0.32%

Time: 16.5s

Precision: binary64

Cost: 1993

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+301}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t_1 + x\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- a t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+301)))
     (+ x (/ y (/ (- a t) (- z t))))
     (+ t_1 x))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (a - t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+301)) {
		tmp = x + (y / ((a - t) / (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 - t));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (a - t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+301)) {
		tmp = x + (y / ((a - t) / (z - t)));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (a - t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+301):
		tmp = x + (y / ((a - t) / (z - t)))
	else:
		tmp = t_1 + x
	return tmp

Julia

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

↓

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(a - t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+301))
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / Float64(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 - t));
end

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (a - t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+301)))
		tmp = x + (y / ((a - t) / (z - t)));
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+301]], $MachinePrecision]], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Target

Original	16.98%
Target	2%
Herbie	0.32%

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < -inf.0 or 2.00000000000000011e301 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

   1. Initial program 98.97

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

   2. Simplified 0.19

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

      [Start] 98.97	\[ x + \frac{y \cdot \left(z - t\right)}{a - t} \]
      associate-/l* [=>] 0.19	\[ x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 2.00000000000000011e301

   1. Initial program 0.35

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

4. Final simplification 0.32

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \leq 2 \cdot 10^{+301}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t} + x\\ \end{array} \]

Alternatives

Alternative 1
Error	34.1%
Cost	1504

\[\begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -3 \cdot 10^{-91}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-134}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-292}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-268}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-194}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-161}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 2
Error	33.91%
Cost	1504

\[\begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{-91}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-137}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-291}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-195}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-160}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 3
Error	28.79%
Cost	1368

\[\begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{a - t}\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;x \leq -2.55 \cdot 10^{+126}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-100}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 4
Error	33.46%
Cost	1240

\[\begin{array}{l} t_1 := z \cdot \frac{y}{a - t}\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{-137}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-290}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-268}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-199}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.06 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 5
Error	21.32%
Cost	1104

\[\begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+45}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+79}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+93}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 6
Error	32.92%
Cost	852

\[\begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-136}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-214}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-290}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 7
Error	32.98%
Cost	852

\[\begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-135}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-214}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-292}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 8
Error	32.92%
Cost	852

\[\begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-137}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-214}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-290}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-268}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 9
Error	22.15%
Cost	844

\[\begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{-15}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-61}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+53}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 10
Error	18.18%
Cost	841

\[\begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+28} \lor \neg \left(t \leq 3.7 \cdot 10^{-60}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \]

Alternative 11
Error	17.27%
Cost	840

\[\begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+28}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 12
Error	17.23%
Cost	840

\[\begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+24}:\\ \;\;\;\;\left(y + x\right) - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 13
Error	3.51%
Cost	836

\[\begin{array}{l} \mathbf{if}\;y \leq 3.5 \cdot 10^{-167}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternative 14
Error	22.02%
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-15}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+26}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 15
Error	4.71%
Cost	704

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

Alternative 16
Error	32.62%
Cost	588

\[\begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-137}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-214}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 17
Error	30.91%
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+144}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Error	42.36%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-125}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-224}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19
Error	45.11%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023088 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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