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

Percentage Accurate: 77.8% → 90.6%

Time: 18.2s

Precision: binary64

Cost: 1096

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+118}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+179}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.5e+118)
   (- x (* z (/ y (- a t))))
   (if (<= t 1.95e+179)
     (+ x (+ y (/ (- t z) (/ (- a t) y))))
     (+ (- x (/ y (/ t a))) (/ y (/ t z))))))

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 tmp;
	if (t <= -2.5e+118) {
		tmp = x - (z * (y / (a - t)));
	} else if (t <= 1.95e+179) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else {
		tmp = (x - (y / (t / a))) + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (x + y) - (((z - t) * y) / (a - t))
end function

↓

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.5d+118)) then
        tmp = x - (z * (y / (a - t)))
    else if (t <= 1.95d+179) then
        tmp = x + (y + ((t - z) / ((a - t) / y)))
    else
        tmp = (x - (y / (t / a))) + (y / (t / z))
    end if
    code = tmp
end function

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 tmp;
	if (t <= -2.5e+118) {
		tmp = x - (z * (y / (a - t)));
	} else if (t <= 1.95e+179) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else {
		tmp = (x - (y / (t / a))) + (y / (t / z));
	}
	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):
	tmp = 0
	if t <= -2.5e+118:
		tmp = x - (z * (y / (a - t)))
	elif t <= 1.95e+179:
		tmp = x + (y + ((t - z) / ((a - t) / y)))
	else:
		tmp = (x - (y / (t / a))) + (y / (t / z))
	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)
	tmp = 0.0
	if (t <= -2.5e+118)
		tmp = Float64(x - Float64(z * Float64(y / Float64(a - t))));
	elseif (t <= 1.95e+179)
		tmp = Float64(x + Float64(y + Float64(Float64(t - z) / Float64(Float64(a - t) / y))));
	else
		tmp = Float64(Float64(x - Float64(y / Float64(t / a))) + Float64(y / Float64(t / z)));
	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)
	tmp = 0.0;
	if (t <= -2.5e+118)
		tmp = x - (z * (y / (a - t)));
	elseif (t <= 1.95e+179)
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	else
		tmp = (x - (y / (t / a))) + (y / (t / z));
	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_] := If[LessEqual[t, -2.5e+118], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+179], N[(x + N[(y + N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	77.8%
Target	88.2%
Herbie	90.6%

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

Derivation

1. Split input into 3 regimes

2. if t < -2.49999999999999986e118

   1. Initial program 48.1%

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

   2. Simplified 85.1%

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

      [Start] 48.1%	\[ \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
      associate--l+ [=>] 55.8%	\[ \color{blue}{x + \left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)} \]
      sub-neg [=>] 55.8%	\[ x + \color{blue}{\left(y + \left(-\frac{\left(z - t\right) \cdot y}{a - t}\right)\right)} \]
      +-commutative [=>] 55.8%	\[ x + \color{blue}{\left(\left(-\frac{\left(z - t\right) \cdot y}{a - t}\right) + y\right)} \]
      associate-/l* [=>] 67.6%	\[ x + \left(\left(-\color{blue}{\frac{z - t}{\frac{a - t}{y}}}\right) + y\right) \]
      distribute-neg-frac [=>] 67.6%	\[ x + \left(\color{blue}{\frac{-\left(z - t\right)}{\frac{a - t}{y}}} + y\right) \]
      associate-/r/ [=>] 85.1%	\[ x + \left(\color{blue}{\frac{-\left(z - t\right)}{a - t} \cdot y} + y\right) \]
      fma-def [=>] 85.1%	\[ x + \color{blue}{\mathsf{fma}\left(\frac{-\left(z - t\right)}{a - t}, y, y\right)} \]
      sub-neg [=>] 85.1%	\[ x + \mathsf{fma}\left(\frac{-\color{blue}{\left(z + \left(-t\right)\right)}}{a - t}, y, y\right) \]
      +-commutative [=>] 85.1%	\[ x + \mathsf{fma}\left(\frac{-\color{blue}{\left(\left(-t\right) + z\right)}}{a - t}, y, y\right) \]
      distribute-neg-in [=>] 85.1%	\[ x + \mathsf{fma}\left(\frac{\color{blue}{\left(-\left(-t\right)\right) + \left(-z\right)}}{a - t}, y, y\right) \]
      unsub-neg [=>] 85.1%	\[ x + \mathsf{fma}\left(\frac{\color{blue}{\left(-\left(-t\right)\right) - z}}{a - t}, y, y\right) \]
      remove-double-neg [=>] 85.1%	\[ x + \mathsf{fma}\left(\frac{\color{blue}{t} - z}{a - t}, y, y\right) \]

   3. Taylor expanded in z around inf 81.2%

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

   4. Simplified 94.0%

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

      [Start] 81.2%	\[ x + -1 \cdot \frac{y \cdot z}{a - t} \]
      mul-1-neg [=>] 81.2%	\[ x + \color{blue}{\left(-\frac{y \cdot z}{a - t}\right)} \]
      *-commutative [=>] 81.2%	\[ x + \left(-\frac{\color{blue}{z \cdot y}}{a - t}\right) \]
      associate-*r/ [<=] 94.0%	\[ x + \left(-\color{blue}{z \cdot \frac{y}{a - t}}\right) \]
      distribute-lft-neg-in [=>] 94.0%	\[ x + \color{blue}{\left(-z\right) \cdot \frac{y}{a - t}} \]

   if -2.49999999999999986e118 < t < 1.94999999999999987e179

   1. Initial program 86.3%

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

   2. Simplified 91.6%

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

      [Start] 86.3%	\[ \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
      associate--l+ [=>] 87.5%	\[ \color{blue}{x + \left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)} \]
      associate-/l* [=>] 91.6%	\[ x + \left(y - \color{blue}{\frac{z - t}{\frac{a - t}{y}}}\right) \]

   if 1.94999999999999987e179 < t

   1. Initial program 33.5%

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

   2. Simplified 38.2%

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

      [Start] 33.5%	\[ \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
      associate-*l/ [<=] 38.2%	\[ \left(x + y\right) - \color{blue}{\frac{z - t}{a - t} \cdot y} \]

   3. Taylor expanded in t around inf 84.6%

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

   4. Simplified 96.0%

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

      [Start] 84.6%	\[ \left(-1 \cdot \frac{y \cdot a}{t} + x\right) - -1 \cdot \frac{y \cdot z}{t} \]
      sub-neg [=>] 84.6%	\[ \color{blue}{\left(-1 \cdot \frac{y \cdot a}{t} + x\right) + \left(--1 \cdot \frac{y \cdot z}{t}\right)} \]
      +-commutative [=>] 84.6%	\[ \color{blue}{\left(x + -1 \cdot \frac{y \cdot a}{t}\right)} + \left(--1 \cdot \frac{y \cdot z}{t}\right) \]
      mul-1-neg [=>] 84.6%	\[ \left(x + \color{blue}{\left(-\frac{y \cdot a}{t}\right)}\right) + \left(--1 \cdot \frac{y \cdot z}{t}\right) \]
      unsub-neg [=>] 84.6%	\[ \color{blue}{\left(x - \frac{y \cdot a}{t}\right)} + \left(--1 \cdot \frac{y \cdot z}{t}\right) \]
      associate-/l* [=>] 88.5%	\[ \left(x - \color{blue}{\frac{y}{\frac{t}{a}}}\right) + \left(--1 \cdot \frac{y \cdot z}{t}\right) \]
      mul-1-neg [=>] 88.5%	\[ \left(x - \frac{y}{\frac{t}{a}}\right) + \left(-\color{blue}{\left(-\frac{y \cdot z}{t}\right)}\right) \]
      remove-double-neg [=>] 88.5%	\[ \left(x - \frac{y}{\frac{t}{a}}\right) + \color{blue}{\frac{y \cdot z}{t}} \]
      associate-/l* [=>] 96.0%	\[ \left(x - \frac{y}{\frac{t}{a}}\right) + \color{blue}{\frac{y}{\frac{t}{z}}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+118}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+179}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	90.6%
Cost	1096

\[\begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+118}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+179}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{\frac{t}{a}}\right) + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 2
Accuracy	90.4%
Cost	1096

\[\begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+118}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+179}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - a}{\frac{t}{y}}\\ \end{array} \]

Alternative 3
Accuracy	81.7%
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-13} \lor \neg \left(a \leq 2.9 \cdot 10^{-101}\right):\\ \;\;\;\;x + \left(y - z \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \]

Alternative 4
Accuracy	82.7%
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-13} \lor \neg \left(a \leq 3.5 \cdot 10^{-101}\right):\\ \;\;\;\;x + \left(y - z \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]

Alternative 5
Accuracy	83.7%
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-5} \lor \neg \left(a \leq 400000000\right):\\ \;\;\;\;x + \left(y - z \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - a}{\frac{t}{y}}\\ \end{array} \]

Alternative 6
Accuracy	84.0%
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-5} \lor \neg \left(a \leq 410000000\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - a}{\frac{t}{y}}\\ \end{array} \]

Alternative 7
Accuracy	88.3%
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+38} \lor \neg \left(a \leq 4.3 \cdot 10^{+36}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 8
Accuracy	77.9%
Cost	713

\[\begin{array}{l} \mathbf{if}\;a \leq -0.09 \lor \neg \left(a \leq 700000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 9
Accuracy	77.2%
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -0.39:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 750000000:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10
Accuracy	77.7%
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -1750:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 430000000:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11
Accuracy	63.9%
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+127}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+180}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Accuracy	51.0%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023263 
(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))))