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

Average Error: 11.2 → 1.4

Time: 18.5s

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	11.2
Target	0.6
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 11.2

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

2. Applied egg-rr 1.4

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

Alternatives

Alternative 1
Error	11.0
Cost	1104

\[\begin{array}{l} t_1 := x + \frac{t}{a - z} \cdot y\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+34}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{t}{z - a} \cdot z\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 2
Error	11.2
Cost	1104

\[\begin{array}{l} t_1 := x + \frac{y}{a - z} \cdot t\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+33}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{t}{z - a} \cdot z\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 3
Error	9.5
Cost	1104

\[\begin{array}{l} t_1 := x + \frac{y}{a - z} \cdot t\\ t_2 := x + \frac{z}{z - a} \cdot t\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{t}{z - a} \cdot z\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	10.1
Cost	1104

\[\begin{array}{l} t_1 := x + \frac{z}{z - a} \cdot t\\ \mathbf{if}\;z \leq -0.00029:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{t}{z - a} \cdot z\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{+153}:\\ \;\;\;\;x + \frac{y}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	9.3
Cost	1036

\[\begin{array}{l} \mathbf{if}\;z \leq -1.1:\\ \;\;\;\;x + \frac{z}{z - a} \cdot t\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{t}{z - a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(-\frac{y - z}{z}\right) \cdot t\\ \end{array} \]

Alternative 6
Error	2.8
Cost	968

\[\begin{array}{l} t_1 := x + \frac{t}{a - z} \cdot \left(y - z\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{-141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-57}:\\ \;\;\;\;x + \frac{z}{z - a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	15.1
Cost	908

\[\begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-7}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{+153}:\\ \;\;\;\;x + \left(-\frac{t}{z} \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 8
Error	15.1
Cost	908

\[\begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-7}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-61}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{+153}:\\ \;\;\;\;x + \left(-\frac{y}{z}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 9
Error	13.8
Cost	908

\[\begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+17}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{t}{a} \cdot \left(y - z\right)\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{+153}:\\ \;\;\;\;x + \left(-\frac{y}{z}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 10
Error	10.8
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+38}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+153}:\\ \;\;\;\;x + \frac{t}{a - z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 11
Error	14.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-7}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{t}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 12
Error	14.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -0.0078:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-91}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 13
Error	22.2
Cost	192

\[x + t \]

Alternative 14
Error	28.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023010 
(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))))