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

Percentage Accurate: 86.3% → 98.1%

Time: 20.0s

Precision: binary64

Cost: 704

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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)) / (z - a))
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
    code = x + (y / ((z - a) / (z - t)))
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	86.3%
Target	98.1%
Herbie	98.1%

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

Derivation

1. Initial program 84.1%

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

2. Simplified 99.1%

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

   [Start] 84.1%	\[ x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   associate-/l* [=>] 99.1%	\[ x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}} \]

3. Final simplification 99.1%

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

Alternatives

Alternative 1
Accuracy	98.1%
Cost	704

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

Alternative 2
Accuracy	72.3%
Cost	1372

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{z - a}\\ \mathbf{if}\;z \leq -8 \cdot 10^{+168}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+55}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -0.64:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-79}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3
Accuracy	73.1%
Cost	1108

\[\begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+152}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -5.1:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-78}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -3.95 \cdot 10^{-168}:\\ \;\;\;\;y \cdot \frac{-t}{z - a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4
Accuracy	81.0%
Cost	1106

\[\begin{array}{l} \mathbf{if}\;z \leq -2400 \lor \neg \left(z \leq -1.75 \cdot 10^{-26} \lor \neg \left(z \leq -1.75 \cdot 10^{-167}\right) \land z \leq 2.7 \cdot 10^{-67}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 5
Accuracy	80.5%
Cost	1104

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{if}\;z \leq -160:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq -2.42 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-68}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Accuracy	59.2%
Cost	977

\[\begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 7.3 \cdot 10^{-63} \lor \neg \left(x \leq 5 \cdot 10^{-11}\right) \land x \leq 3300:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Accuracy	59.2%
Cost	976

\[\begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-66}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-62}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 140:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Accuracy	94.1%
Cost	969

\[\begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-226} \lor \neg \left(x \leq 1.7 \cdot 10^{-151}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \end{array} \]

Alternative 9
Accuracy	59.6%
Cost	848

\[\begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-79}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-280}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-169}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10
Accuracy	74.8%
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+152}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -8.3 \cdot 10^{-168}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11
Accuracy	78.6%
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -1.18 \cdot 10^{+47} \lor \neg \left(a \leq 9 \cdot 10^{+72}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \end{array} \]

Alternative 12
Accuracy	82.1%
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+20} \lor \neg \left(a \leq 3.7 \cdot 10^{+88}\right):\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \]

Alternative 13
Accuracy	87.2%
Cost	841

\[\begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-66} \lor \neg \left(t \leq 1.32 \cdot 10^{-39}\right):\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]

Alternative 14
Accuracy	75.9%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-96}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+26}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 15
Accuracy	63.7%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-151}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 16
Accuracy	59.8%
Cost	452

\[\begin{array}{l} \mathbf{if}\;t \leq 2.2 \cdot 10^{+145}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 17
Accuracy	53.7%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{-114}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-149}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Accuracy	51.3%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023263 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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