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

Average Accuracy: 83.8% → 97.9%

Time: 12.2s

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	83.8%
Target	97.9%
Herbie	97.9%

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

Derivation

1. Initial program 83.8%

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

2. Simplified 97.9%

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

   [Start] 83.8	\[ x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   associate-/l* [=>] 97.9	\[ x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

3. Final simplification 97.9%

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

Alternatives

Alternative 1
Accuracy	65.2%
Cost	1240

\[\begin{array}{l} t_1 := z \cdot \frac{y}{a - t}\\ \mathbf{if}\;t \leq -1.66 \cdot 10^{-65}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-191}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-210}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{-239}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 490:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 2
Accuracy	64.3%
Cost	1240

\[\begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;t \leq -2.95 \cdot 10^{-65}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-134}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-195}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-302}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 14.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3
Accuracy	81.5%
Cost	1105

\[\begin{array}{l} t_1 := x - t \cdot \frac{y}{a - t}\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-153}:\\ \;\;\;\;x - \frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-191} \lor \neg \left(t \leq 1.35 \cdot 10^{+28}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 4
Accuracy	76.4%
Cost	976

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;t \leq -2.05 \cdot 10^{+37}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 270000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5
Accuracy	79.2%
Cost	841

\[\begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+32} \lor \neg \left(t \leq 9 \cdot 10^{+68}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 6
Accuracy	81.8%
Cost	841

\[\begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+28} \lor \neg \left(t \leq 4.7 \cdot 10^{+86}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 7
Accuracy	76.9%
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+36}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+86}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8
Accuracy	95.1%
Cost	704

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

Alternative 9
Accuracy	67.4%
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+77}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 215:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10
Accuracy	54.5%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023133 
(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))))