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

Average Accuracy: 83.1% → 98.1%

Time: 13.1s

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	83.1%
Target	98.1%
Herbie	98.1%

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

Derivation

1. Initial program 83.1%

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

2. Simplified 98.1%

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

   [Start] 83.1	\[ x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   associate-/l* [=>] 98.1	\[ x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

3. Final simplification 98.1%

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

Alternatives

Alternative 1
Accuracy	68.3%
Cost	1240

\[\begin{array}{l} t_1 := z \cdot \frac{y}{a - t}\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+111}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-223}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+52}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 2
Accuracy	60.9%
Cost	976

\[\begin{array}{l} t_1 := z \cdot \frac{y}{a - t}\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{-67}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-223}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+71}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Accuracy	77.1%
Cost	976

\[\begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -5.1 \cdot 10^{+35}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4
Accuracy	85.0%
Cost	972

\[\begin{array}{l} t_1 := x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-29}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 5
Accuracy	96.1%
Cost	969

\[\begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-141} \lor \neg \left(z \leq 8 \cdot 10^{-212}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \end{array} \]

Alternative 6
Accuracy	83.6%
Cost	841

\[\begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-20} \lor \neg \left(t \leq 21000000000000\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \]

Alternative 7
Accuracy	79.6%
Cost	840

\[\begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+37}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8
Accuracy	77.7%
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+35}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+15}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9
Accuracy	69.3%
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-29}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 33500000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10
Accuracy	57.0%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-79}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Accuracy	55.6%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023138 
(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))))