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

Average Error: 11.2 → 0.7

Time: 8.7s

Precision: binary64

Cost: 968

Math

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

↓

\[\begin{array}{l} t_1 := x + t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -0.0002:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-209}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ (- y z) (- a z))))))
   (if (<= t -0.0002)
     t_1
     (if (<= t 5e-209) (+ x (/ (* t (- y z)) (- a z))) t_1))))

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) {
	double t_1 = x + (t * ((y - z) / (a - z)));
	double tmp;
	if (t <= -0.0002) {
		tmp = t_1;
	} else if (t <= 5e-209) {
		tmp = x + ((t * (y - z)) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t * ((y - z) / (a - z)))
    if (t <= (-0.0002d0)) then
        tmp = t_1
    else if (t <= 5d-209) then
        tmp = x + ((t * (y - z)) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
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) {
	double t_1 = x + (t * ((y - z) / (a - z)));
	double tmp;
	if (t <= -0.0002) {
		tmp = t_1;
	} else if (t <= 5e-209) {
		tmp = x + ((t * (y - z)) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	t_1 = x + (t * ((y - z) / (a - z)))
	tmp = 0
	if t <= -0.0002:
		tmp = t_1
	elif t <= 5e-209:
		tmp = x + ((t * (y - z)) / (a - z))
	else:
		tmp = t_1
	return tmp

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)
	t_1 = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))))
	tmp = 0.0
	if (t <= -0.0002)
		tmp = t_1;
	elseif (t <= 5e-209)
		tmp = Float64(x + Float64(Float64(t * Float64(y - z)) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * ((y - z) / (a - z)));
	tmp = 0.0;
	if (t <= -0.0002)
		tmp = t_1;
	elseif (t <= 5e-209)
		tmp = x + ((t * (y - z)) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
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_] := Block[{t$95$1 = N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.0002], t$95$1, If[LessEqual[t, 5e-209], N[(x + N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Target

Original	11.2
Target	0.5
Herbie	0.7

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

Derivation

1. Split input into 2 regimes

2. if t < -2.0000000000000001e-4 or 5.0000000000000005e-209 < t

   1. Initial program 17.4

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

   2. Simplified 0.9

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot t} \]
      Proof
      (+.f64 x (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)): 0 points increase in error, 0 points decrease in error
      (+.f64 x (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))): 58 points increase in error, 15 points decrease in error

   if -2.0000000000000001e-4 < t < 5.0000000000000005e-209

   1. Initial program 0.2

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0002:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-209}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternatives

Alternative 1
Error	10.1
Cost	1236

\[\begin{array}{l} t_1 := x - \frac{t}{\frac{a}{z} + -1}\\ t_2 := x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-213}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-286}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	13.2
Cost	1104

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+23}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-286}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 3
Error	12.7
Cost	1104

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{+26}:\\ \;\;\;\;x + \frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-285}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 245000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 4
Error	23.6
Cost	976

\[\begin{array}{l} t_1 := y \cdot \frac{t}{a - z}\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{-169}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-245}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 5
Error	22.8
Cost	976

\[\begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-168}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-308}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{-184}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-106}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 6
Error	14.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+23}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 86000000:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 7
Error	1.5
Cost	704

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

Alternative 8
Error	19.6
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-35}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 10^{-39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 9
Error	27.2
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{-176}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Error	50.7
Cost	64

\[t \]

Reproduce

herbie shell --seed 2022329 
(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))))