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

Average Error: 10.8 → 1.4

Time: 9.4s

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	10.8
Target	0.5
Herbie	1.4

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

Derivation

1. Initial program 10.8

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

2. Simplified 1.4

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

   [Start] 10.8	\[ x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   associate-*l/ [<=] 1.4	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

3. Final simplification 1.4

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

Alternatives

Alternative 1
Error	14.6
Cost	1104

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-66}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-24}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+87}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+94}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 2
Error	11.9
Cost	973

\[\begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+177}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-81} \lor \neg \left(z \leq 7.5 \cdot 10^{-23}\right):\\ \;\;\;\;x + \frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 3
Error	12.4
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-81} \lor \neg \left(z \leq 2.9 \cdot 10^{-23}\right):\\ \;\;\;\;x + \frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 4
Error	14.1
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-63} \lor \neg \left(z \leq 3.8 \cdot 10^{+29}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 5
Error	14.1
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-63} \lor \neg \left(z \leq 4.8 \cdot 10^{+26}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 6
Error	20.8
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-63}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-154}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 7
Error	19.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-146}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 8
Error	27.4
Cost	328

\[\begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+97}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9
Error	50.8
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023018 
(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))))