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

Average Error: 16.55% → 0.35%

Time: 12.0s

Precision: binary64

Cost: 1992

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+282}:\\ \;\;\;\;t_1 + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \]

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 (<= t_1 (- INFINITY))
     (+ x (/ (- y z) (/ (- a z) t)))
     (if (<= t_1 5e+282) (+ t_1 x) (+ x (* t (/ (- y z) (- a z))))))))

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)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else if (t_1 <= 5e+282) {
		tmp = t_1 + x;
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	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) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else if (t_1 <= 5e+282) {
		tmp = t_1 + x;
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	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:
		tmp = x + ((y - z) / ((a - z) / t))
	elif t_1 <= 5e+282:
		tmp = t_1 + x
	else:
		tmp = x + (t * ((y - z) / (a - z)))
	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))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	elseif (t_1 <= 5e+282)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	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)
		tmp = x + ((y - z) / ((a - z) / t));
	elseif (t_1 <= 5e+282)
		tmp = t_1 + x;
	else
		tmp = x + (t * ((y - z) / (a - z)));
	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[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+282], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	16.55%
Target	0.82%
Herbie	0.35%

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 100

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

   2. Simplified 0.23

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

      [Start] 100	\[ x + \frac{\left(y - z\right) \cdot t}{a - z} \]
      associate-/l* [=>] 0.23	\[ x + \color{blue}{\frac{y - z}{\frac{a - z}{t}}} \]

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 4.99999999999999978e282

   1. Initial program 0.32

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

   if 4.99999999999999978e282 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 94.2

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

   2. Simplified 0.76

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

      [Start] 94.2	\[ x + \frac{\left(y - z\right) \cdot t}{a - z} \]
      associate-*l/ [<=] 0.76	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

3. Recombined 3 regimes into one program.

4. Final simplification 0.35

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 5 \cdot 10^{+282}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternatives

Alternative 1
Error	0.85%
Cost	1993

\[\begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+174} \lor \neg \left(t_1 \leq 5 \cdot 10^{+282}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1 + x\\ \end{array} \]

Alternative 2
Error	24.21%
Cost	1896

\[\begin{array}{l} t_1 := x - \frac{z \cdot t}{a - z}\\ t_2 := \frac{t}{\frac{a - z}{y - z}}\\ t_3 := x + y \cdot \frac{t}{a - z}\\ \mathbf{if}\;t \leq -6 \cdot 10^{+248}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+183}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-140}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-146}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{+180}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+251}:\\ \;\;\;\;\frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	20.54%
Cost	1501

\[\begin{array}{l} t_1 := x - \frac{z \cdot t}{a - z}\\ t_2 := x + y \cdot \frac{t}{a - z}\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{-48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-144}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-58}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+78} \lor \neg \left(y \leq 2.05 \cdot 10^{+123}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 4
Error	16.41%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+98} \lor \neg \left(z \leq 2 \cdot 10^{+104}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]

Alternative 5
Error	23.12%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+15} \lor \neg \left(z \leq 1.05 \cdot 10^{+104}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 6
Error	23.03%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+16}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+103}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 7
Error	2.16%
Cost	704

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

Alternative 8
Error	30.59%
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+195}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Error	41.38%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-165}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.62 \cdot 10^{-69}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Error	79.95%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023121 
(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))))