Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3

Average Error: 24.5 → 9.0

Time: 17.0s

Precision: binary64

Cost: 4432

Math

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

↓

\[\begin{array}{l} t_1 := \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-298}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y + \left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+296}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- (/ z (- a t)) (/ t (- a t))) y))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-298)
       t_2
       (if (<= t_2 0.0)
         (+ y (- (/ (* (- y x) (- z a)) t)))
         (if (<= t_2 5e+296) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}

↓

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z / (a - t)) - (t / (a - t))) * y;
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-298) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + -(((y - x) * (z - a)) / t);
	} else if (t_2 <= 5e+296) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z / (a - t)) - (t / (a - t))) * y;
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-298) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + -(((y - x) * (z - a)) / t);
	} else if (t_2 <= 5e+296) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	t_1 = ((z / (a - t)) - (t / (a - t))) * y
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-298:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + -(((y - x) * (z - a)) / t)
	elif t_2 <= 5e+296:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
end

↓

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z / Float64(a - t)) - Float64(t / Float64(a - t))) * y)
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-298)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(-Float64(Float64(Float64(y - x) * Float64(z - a)) / t)));
	elseif (t_2 <= 5e+296)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((z / (a - t)) - (t / (a - t))) * y;
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-298)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + -(((y - x) * (z - a)) / t);
	elseif (t_2 <= 5e+296)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-298], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + (-N[(N[(N[(y - x), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision])), $MachinePrecision], If[LessEqual[t$95$2, 5e+296], t$95$2, t$95$1]]]]]]

Target

Original	24.5
Target	9.6
Herbie	9.0

\[\begin{array}{l} \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 5.0000000000000001e296 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 62.5

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

   2. Taylor expanded in y around inf 26.5

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.99999999999999982e-298 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 5.0000000000000001e296

   1. Initial program 2.0

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

   if -1.99999999999999982e-298 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 60.9

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

   2. Taylor expanded in t around -inf 0.5

      \[\leadsto \color{blue}{y + -1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]

   3. Simplified 0.5

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

      [Start] 0.5	\[ y + -1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.5	\[ y + \color{blue}{\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t} \cdot -1} \]
      rational_best_oopsla_all_46_json_45_simplify-92 [=>] 0.5	\[ y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [<=] 0.5	\[ y + \left(-\frac{\color{blue}{z \cdot \left(y - x\right)} - a \cdot \left(y - x\right)}{t}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.5	\[ y + \left(-\frac{z \cdot \left(y - x\right) - \color{blue}{\left(y - x\right) \cdot a}}{t}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-102 [=>] 0.5	\[ y + \left(-\frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t}\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 9.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-298}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+296}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y\\ \end{array} \]

Alternatives

Alternative 1
Error	32.7
Cost	2092

\[\begin{array}{l} t_1 := y + \left(-\frac{\left(y - x\right) \cdot z}{t}\right)\\ t_2 := \frac{y \cdot \left(z - t\right)}{a - t}\\ t_3 := x + x \cdot \left(-\frac{z}{a - t}\right)\\ t_4 := \frac{\left(z - t\right) \cdot y}{a} + x\\ \mathbf{if}\;x \leq -5.6 \cdot 10^{+51}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-187}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-241}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{elif}\;x \leq -2.95 \cdot 10^{-298}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-120}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+240}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+271}:\\ \;\;\;\;\frac{\left(z - a\right) \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Error	32.8
Cost	2092

\[\begin{array}{l} t_1 := y + \left(-\frac{\left(y - x\right) \cdot z}{t}\right)\\ t_2 := x + x \cdot \left(-\frac{z}{a - t}\right)\\ t_3 := \frac{\left(z - t\right) \cdot y}{a} + x\\ t_4 := \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-187}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-241}:\\ \;\;\;\;y + y \cdot \left(-\frac{z - a}{t}\right)\\ \mathbf{elif}\;x \leq -2.95 \cdot 10^{-298}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-196}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-121}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+242}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+271}:\\ \;\;\;\;\frac{\left(z - a\right) \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	20.9
Cost	1296

\[\begin{array}{l} t_1 := x + \frac{\left(z - t\right) \cdot y}{a - t}\\ t_2 := y + \left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)\\ \mathbf{if}\;t \leq -0.0165:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.55 \cdot 10^{-208}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	21.6
Cost	1232

\[\begin{array}{l} t_1 := x + \frac{\left(z - t\right) \cdot y}{a - t}\\ t_2 := \left(y - x\right) \cdot z\\ t_3 := y + \left(-\frac{t_2}{t}\right)\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+19}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-208}:\\ \;\;\;\;x + \frac{t_2}{a - t}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 5
Error	28.0
Cost	1036

\[\begin{array}{l} t_1 := y - y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -165000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-281}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a} + x\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+82}:\\ \;\;\;\;x + x \cdot \left(-\frac{z}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	22.2
Cost	968

\[\begin{array}{l} t_1 := \left(y - x\right) \cdot z\\ t_2 := y + \left(-\frac{t_1}{t}\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{t_1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	37.0
Cost	912

\[\begin{array}{l} \mathbf{if}\;t \leq -1900000000:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+113}:\\ \;\;\;\;\frac{z \cdot x}{t}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+161}:\\ \;\;\;\;\frac{a}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8
Error	32.3
Cost	912

\[\begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+16}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+31}:\\ \;\;\;\;\frac{y \cdot z}{a} + x\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+109}:\\ \;\;\;\;\frac{z \cdot x}{t}\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+160}:\\ \;\;\;\;\frac{a}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9
Error	29.7
Cost	908

\[\begin{array}{l} t_1 := y - y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -130000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-281}:\\ \;\;\;\;\frac{y \cdot z}{a} + x\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+56}:\\ \;\;\;\;\left(-1 + \frac{z}{a}\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	27.0
Cost	840

\[\begin{array}{l} t_1 := y - y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -190000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	26.9
Cost	840

\[\begin{array}{l} t_1 := y - y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -105000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+52}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a} + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	27.1
Cost	840

\[\begin{array}{l} t_1 := y - y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -205000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+40}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	28.8
Cost	712

\[\begin{array}{l} t_1 := y - y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -170000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+41}:\\ \;\;\;\;\frac{y \cdot z}{a} + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	35.6
Cost	328

\[\begin{array}{l} \mathbf{if}\;t \leq -380000000:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 15
Error	45.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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