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

Average Accuracy: 98.2% → 98.2%

Time: 11.0s

Precision: binary64

Cost: 704

Math

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

↓

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

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 t) (- z a)))))

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 - t) / (z - a)));
}

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 - t) / (z - a)))
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 - t) / (z - a)));
}

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 - t) / (z - a)))

Julia

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

↓

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

Wolfram

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

↓

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

Target

Original	98.2%
Target	98.3%
Herbie	98.2%

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

Derivation

1. Initial program 98.2%

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

2. Final simplification 98.2%

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

Alternatives

Alternative 1
Accuracy	75.0%
Cost	3152

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-240}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t_1 \leq 10^{-246}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-58}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	74.8%
Cost	3152

\[\begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{z - a}\\ t_2 := y \cdot \frac{z - t}{z - a}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-240}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t_2 \leq 10^{-246}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-44}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Accuracy	79.8%
Cost	1865

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+33} \lor \neg \left(t_1 \leq 5 \cdot 10^{-44}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 4
Accuracy	78.0%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-31}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-38}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5
Accuracy	69.0%
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+150}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+155}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Accuracy	57.7%
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+70}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+167}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7
Accuracy	54.9%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023141 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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