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

Average Error: 10.5 → 1.3

Time: 16.1s

Precision: binary64

Cost: 960

Math

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

↓

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

FPCore

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

↓

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

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

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 = (((z / (a - t)) - (t / (a - t))) * y) + x
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 (((z / (a - t)) - (t / (a - t))) * y) + x;
}

Python

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

↓

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

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(Float64(Float64(Float64(z / Float64(a - t)) - Float64(t / Float64(a - t))) * y) + x)
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 = (((z / (a - t)) - (t / (a - t))) * y) + x;
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[(N[(N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] + x), $MachinePrecision]

Target

Original	10.5
Target	1.2
Herbie	1.3

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

Derivation

1. Initial program 10.5

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

2. Taylor expanded in y around 0 1.3

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

3. Final simplification 1.3

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

Alternatives

Alternative 1
Error	3.2
Cost	2120

\[\begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t_1 \leq 10^{+223}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y\\ \end{array} \]

Alternative 2
Error	3.6
Cost	1992

\[\begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+291}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{z}{t}\right) \cdot y + x\\ \end{array} \]

Alternative 3
Error	14.7
Cost	976

\[\begin{array}{l} t_1 := \frac{z}{a} \cdot y + x\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+72}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -1.55:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-78}:\\ \;\;\;\;\left(-\frac{y \cdot z}{t}\right) + x\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 4
Error	11.7
Cost	840

\[\begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+72}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+45}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 5
Error	9.6
Cost	840

\[\begin{array}{l} t_1 := \left(1 - \frac{z}{t}\right) \cdot y + x\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+45}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	8.9
Cost	840

\[\begin{array}{l} t_1 := \left(1 - \frac{z}{t}\right) \cdot y + x\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+44}:\\ \;\;\;\;\frac{z}{a - t} \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	14.4
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+72}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-15}:\\ \;\;\;\;\frac{z}{a} \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 8
Error	19.8
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+114}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+85}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Error	27.1
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -1.34 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-216}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Error	28.2
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023077 
(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))))