Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A

Average Accuracy: 82.7% → 97.5%

Time: 12.3s

Precision: binary64

Cost: 704

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	82.7%
Target	99.0%
Herbie	97.5%

\[\begin{array}{l} \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array} \]

Derivation

1. Initial program 82.7%

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

2. Simplified 97.5%

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

   [Start] 82.7	\[ x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   associate-*l/ [<=] 97.5	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

3. Final simplification 97.5%

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

Alternatives

Alternative 1
Accuracy	72.2%
Cost	1104

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;x \leq -4.1 \cdot 10^{-71}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-73}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;x \leq 0.0036:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 2
Accuracy	78.4%
Cost	1104

\[\begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+72}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-68}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+32}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+90}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 3
Accuracy	63.9%
Cost	977

\[\begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-144}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-265} \lor \neg \left(x \leq 3 \cdot 10^{-296}\right) \land x \leq 7.8 \cdot 10^{-258}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 4
Accuracy	62.6%
Cost	849

\[\begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-145}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-267} \lor \neg \left(x \leq 3.3 \cdot 10^{-296}\right) \land x \leq 8 \cdot 10^{-259}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 5
Accuracy	80.6%
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+54} \lor \neg \left(a \leq 32000000000000\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{t}{z}\\ \end{array} \]

Alternative 6
Accuracy	84.8%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-115} \lor \neg \left(z \leq 3 \cdot 10^{-32}\right):\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \end{array} \]

Alternative 7
Accuracy	81.0%
Cost	841

\[\begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-84} \lor \neg \left(x \leq 3.2 \cdot 10^{-154}\right):\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 8
Accuracy	77.9%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+31}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 9
Accuracy	68.9%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-98}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 10
Accuracy	57.0%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-133}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Accuracy	20.5%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023140 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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