Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4

Average Accuracy: 96.4% → 96.4%

Time: 8.7s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

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

C

double code(double x, double y, double z, double t) {
	return x + ((y - x) * (z / t));
}

↓

double code(double x, double y, double z, double t) {
	return x + ((y - x) * (z / t));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((y - x) * (z / t))
end function

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((y - x) * (z / t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + ((y - x) * (z / t));
}

↓

public static double code(double x, double y, double z, double t) {
	return x + ((y - x) * (z / t));
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	96.4%
Target	96.2%
Herbie	96.4%

\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} < -1013646692435.8867:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} < 0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \]

Derivation

1. Initial program 96.4%

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

2. Final simplification 96.4%

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

Alternatives

Alternative 1
Accuracy	65.4%
Cost	1361

\[\begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -2000000000:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-41} \lor \neg \left(\frac{z}{t} \leq 10^{-18}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Accuracy	65.4%
Cost	1361

\[\begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -2000000000:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-41} \lor \neg \left(\frac{z}{t} \leq 10^{-18}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Accuracy	80.4%
Cost	969

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{+161} \lor \neg \left(\frac{z}{t} \leq -2 \cdot 10^{+88}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \end{array} \]

Alternative 4
Accuracy	92.8%
Cost	969

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2000 \lor \neg \left(\frac{z}{t} \leq 20000000000000\right):\\ \;\;\;\;\frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 5
Accuracy	95.0%
Cost	969

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2000 \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 6
Accuracy	92.2%
Cost	968

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2000000000:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 20000000000000:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 7
Accuracy	65.0%
Cost	841

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-41} \lor \neg \left(\frac{z}{t} \leq 10^{-18}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Accuracy	85.1%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-165} \lor \neg \left(y \leq 2.6 \cdot 10^{-187}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{t}\\ \end{array} \]

Alternative 9
Accuracy	50.5%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023135 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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