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

Average Error: 10.6 → 1.6

Time: 10.3s

Precision: binary64

Cost: 832

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (+ x (* y (/ 1.0 (/ (- a t) (- z t))))))

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) {
	return x + (y * (1.0 / ((a - t) / (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)) / (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
    code = x + (y * (1.0d0 / ((a - t) / (z - t))))
end function

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) {
	return x + (y * (1.0 / ((a - t) / (z - t))));
}

Python

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

↓

def code(x, y, z, t, a):
	return x + (y * (1.0 / ((a - t) / (z - t))))

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)
	return Float64(x + Float64(y * Float64(1.0 / Float64(Float64(a - t) / Float64(z - t)))))
end

MATLAB

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

↓

function tmp = code(x, y, z, t, a)
	tmp = x + (y * (1.0 / ((a - t) / (z - t))));
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_] := N[(x + N[(y * N[(1.0 / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	10.6
Target	1.4
Herbie	1.6

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

Derivation

1. Initial program 10.6

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

2. Applied egg-rr 1.6

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

3. Final simplification 1.6

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

Alternatives

Alternative 1
Error	2.5
Cost	1992

\[\begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+295}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{t - a}\\ \end{array} \]

Alternative 2
Error	10.9
Cost	840

\[\begin{array}{l} t_1 := x - \frac{y}{\frac{a - t}{t}}\\ \mathbf{if}\;t \leq -4.071511416001858 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.838753382168689 \cdot 10^{-153}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	8.5
Cost	840

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{if}\;z \leq -1.8806392455483117 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.417193312800827 \cdot 10^{+109}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	19.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -2.2809849630464558 \cdot 10^{+53}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.283819516414495 \cdot 10^{-61}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5
Error	19.1
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -2.2809849630464558 \cdot 10^{+53}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.283819516414495 \cdot 10^{-61}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Error	14.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -2.2809849630464558 \cdot 10^{+53}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.283819516414495 \cdot 10^{-61}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7
Error	14.4
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -2.2809849630464558 \cdot 10^{+53}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.283819516414495 \cdot 10^{-61}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8
Error	19.5
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -1.985141535833203 \cdot 10^{-93}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.462849520098056 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9
Error	28.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022317 
(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))))