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

Average Error: 10.8 → 4.2

Time: 9.7s

Precision: binary64

Cost: 2120

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t_1 \leq 10^{+264}:\\ \;\;\;\;x + \frac{y \cdot t - z \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

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 (/ (* (- y z) t) (- a z))))
   (if (<= t_1 (- INFINITY))
     (+ x t)
     (if (<= t_1 1e+264) (+ x (/ (- (* y t) (* z t)) (- a z))) (+ x 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) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + t;
	} else if (t_1 <= 1e+264) {
		tmp = x + (((y * t) - (z * t)) / (a - z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

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 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + t;
	} else if (t_1 <= 1e+264) {
		tmp = x + (((y * t) - (z * t)) / (a - z));
	} else {
		tmp = x + t;
	}
	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 = ((y - z) * t) / (a - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + t
	elif t_1 <= 1e+264:
		tmp = x + (((y * t) - (z * t)) / (a - z))
	else:
		tmp = x + t
	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(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + t);
	elseif (t_1 <= 1e+264)
		tmp = Float64(x + Float64(Float64(Float64(y * t) - Float64(z * t)) / Float64(a - z)));
	else
		tmp = Float64(x + t);
	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 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + t;
	elseif (t_1 <= 1e+264)
		tmp = x + (((y * t) - (z * t)) / (a - z));
	else
		tmp = x + t;
	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[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + t), $MachinePrecision], If[LessEqual[t$95$1, 1e+264], N[(x + N[(N[(N[(y * t), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Target

Original	10.8
Target	0.6
Herbie	4.2

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0 or 1.00000000000000004e264 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 60.8

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

   2. Taylor expanded in z around inf 23.3

      \[\leadsto x + \color{blue}{t} \]

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 1.00000000000000004e264

   1. Initial program 0.2

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

   2. Applied egg-rr 0.2

      \[\leadsto x + \frac{\color{blue}{y \cdot t - z \cdot t}}{a - z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 4.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty:\\ \;\;\;\;x + t\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 10^{+264}:\\ \;\;\;\;x + \frac{y \cdot t - z \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternatives

Alternative 1
Error	4.2
Cost	1992

\[\begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t_1 \leq 10^{+264}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 2
Error	16.8
Cost	1368

\[\begin{array}{l} t_1 := x + \frac{y \cdot t}{a - z}\\ t_2 := t \cdot \frac{y}{a} + x\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-66}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-213}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+28}:\\ \;\;\;\;x + \left(t + \frac{t \cdot a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	15.0
Cost	1368

\[\begin{array}{l} t_1 := x + \frac{y \cdot t}{a - z}\\ t_2 := t \cdot \frac{y - z}{a} + x\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-67}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-213}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+33}:\\ \;\;\;\;x + \left(t + \frac{t \cdot a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	15.1
Cost	1236

\[\begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-33}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-142}:\\ \;\;\;\;t \cdot \frac{y}{a} + x\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-185}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a}\right) + x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-63}:\\ \;\;\;\;t \cdot \left(\frac{y}{a} - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 5
Error	14.5
Cost	1108

\[\begin{array}{l} t_1 := t \cdot \frac{y}{a} + x\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{-30}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-185}:\\ \;\;\;\;\left(-\frac{t \cdot z}{a}\right) + x\\ \mathbf{elif}\;z \leq 10^{-280}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 6
Error	14.5
Cost	1108

\[\begin{array}{l} t_1 := t \cdot \frac{y}{a} + x\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{-31}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-185}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a}\right) + x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-267}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 7
Error	14.0
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+43}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 8
Error	15.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-122}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.76 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 9
Error	14.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-32}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \frac{y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 10
Error	19.6
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-122}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 11
Error	28.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023090 
(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))))