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

Average Error: 10.6 → 1.2

Time: 11.4s

Precision: binary64

Cost: 704

Math

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

↓

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

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 (/ (- 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 / ((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 / ((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 / ((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 / ((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(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 / ((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[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	10.6
Target	1.2
Herbie	1.2

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

Derivation

1. Initial program 10.6

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

2. Simplified 1.2

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

   [Start] 10.6	\[ x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   associate-/l* [=>] 1.2	\[ x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

3. Final simplification 1.2

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

Alternatives

Alternative 1
Error	12.7
Cost	1500

\[\begin{array}{l} t_1 := x - t \cdot \frac{y}{a - t}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ t_3 := x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{if}\;y \leq -1.08 \cdot 10^{+145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-80}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-118}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+47}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.48 \cdot 10^{+218}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	22.3
Cost	977

\[\begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-240}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-307} \lor \neg \left(x \leq 1.8 \cdot 10^{-253}\right) \land x \leq 5.2 \cdot 10^{-219}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3
Error	10.3
Cost	841

\[\begin{array}{l} \mathbf{if}\;t \leq -8.4 \cdot 10^{+96} \lor \neg \left(t \leq 2.1 \cdot 10^{+78}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \end{array} \]

Alternative 4
Error	8.5
Cost	841

\[\begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+37} \lor \neg \left(t \leq 2.4 \cdot 10^{-16}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \end{array} \]

Alternative 5
Error	8.7
Cost	840

\[\begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{-82}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-16}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \end{array} \]

Alternative 6
Error	3.1
Cost	836

\[\begin{array}{l} \mathbf{if}\;t \leq 8 \cdot 10^{+131}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \end{array} \]

Alternative 7
Error	15.2
Cost	713

\[\begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-82} \lor \neg \left(t \leq 4.1 \cdot 10^{-122}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 8
Error	22.7
Cost	584

\[\begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-226}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-286}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9
Error	22.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-227}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-287}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10
Error	20.7
Cost	324

\[\begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11
Error	28.4
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023039 
(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))))