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

Average Error: 25.2 → 18.0

Time: 15.3s

Precision: binary64

Cost: 968

Math

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

↓

\[\begin{array}{l} t_1 := x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{if}\;a \leq -1.126403446567394 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.0224009117846062 \cdot 10^{+37}:\\ \;\;\;\;y + \frac{a - z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 (+ x (* (/ y a) (- z t)))))
   (if (<= a -1.126403446567394e+45)
     t_1
     (if (<= a 1.0224009117846062e+37) (+ y (* (/ (- a z) t) (- y x))) 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 = x + ((y / a) * (z - t));
	double tmp;
	if (a <= -1.126403446567394e+45) {
		tmp = t_1;
	} else if (a <= 1.0224009117846062e+37) {
		tmp = y + (((a - z) / t) * (y - x));
	} 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 - x) * (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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y / a) * (z - t))
    if (a <= (-1.126403446567394d+45)) then
        tmp = t_1
    else if (a <= 1.0224009117846062d+37) then
        tmp = y + (((a - z) / t) * (y - x))
    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 - x) * (z - t)) / (a - t));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y / a) * (z - t));
	double tmp;
	if (a <= -1.126403446567394e+45) {
		tmp = t_1;
	} else if (a <= 1.0224009117846062e+37) {
		tmp = y + (((a - z) / t) * (y - x));
	} 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 = x + ((y / a) * (z - t))
	tmp = 0
	if a <= -1.126403446567394e+45:
		tmp = t_1
	elif a <= 1.0224009117846062e+37:
		tmp = y + (((a - z) / t) * (y - x))
	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(x + Float64(Float64(y / a) * Float64(z - t)))
	tmp = 0.0
	if (a <= -1.126403446567394e+45)
		tmp = t_1;
	elseif (a <= 1.0224009117846062e+37)
		tmp = Float64(y + Float64(Float64(Float64(a - z) / t) * Float64(y - x)));
	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 = x + ((y / a) * (z - t));
	tmp = 0.0;
	if (a <= -1.126403446567394e+45)
		tmp = t_1;
	elseif (a <= 1.0224009117846062e+37)
		tmp = y + (((a - z) / t) * (y - x));
	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[(x + N[(N[(y / a), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.126403446567394e+45], t$95$1, If[LessEqual[a, 1.0224009117846062e+37], N[(y + N[(N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Target

Original	25.2
Target	9.2
Herbie	18.0

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

Derivation

1. Split input into 2 regimes

2. if a < -1.126403446567394e45 or 1.02240091178460618e37 < a

   1. Initial program 22.9

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

   2. Applied egg-rr 5.8

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

   3. Taylor expanded in a around inf 27.0

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

   4. Simplified 15.0

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

   5. Taylor expanded in y around inf 25.4

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

   6. Simplified 19.5

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

   if -1.126403446567394e45 < a < 1.02240091178460618e37

   1. Initial program 27.4

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

   2. Simplified 17.8

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   3. Taylor expanded in t around inf 21.5

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

   4. Simplified 16.6

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

4. Final simplification 18.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.126403446567394 \cdot 10^{+45}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{elif}\;a \leq 1.0224009117846062 \cdot 10^{+37}:\\ \;\;\;\;y + \frac{a - z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	32.9
Cost	1436

\[\begin{array}{l} t_1 := \frac{x}{t} \cdot \left(z - a\right)\\ t_2 := \frac{y}{\frac{a - t}{-t}}\\ \mathbf{if}\;t \leq -1.7602622053992855 \cdot 10^{+257}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.584847870241093 \cdot 10^{+235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.5857366654332107 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-121}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;t \leq 2.8477742541146235 \cdot 10^{+22}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.1687612796200853 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.3644462080535163 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	28.6
Cost	1368

\[\begin{array}{l} t_1 := \frac{y}{\frac{a - t}{-t}}\\ \mathbf{if}\;t \leq -1.7602622053992855 \cdot 10^{+257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.584847870241093 \cdot 10^{+235}:\\ \;\;\;\;\frac{x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;t \leq -2.3730116082999515 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{z}{\frac{-t}{y - x}}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{t - z}{\frac{a - t}{x}}\\ \mathbf{elif}\;t \leq 2.8477742541146235 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	34.4
Cost	1108

\[\begin{array}{l} \mathbf{if}\;t \leq -1.7602622053992855 \cdot 10^{+257}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.584847870241093 \cdot 10^{+235}:\\ \;\;\;\;\frac{x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;t \leq -1.5857366654332107 \cdot 10^{+61}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-121}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;t \leq 3.4526091493963727 \cdot 10^{+36}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 4
Error	26.8
Cost	1104

\[\begin{array}{l} t_1 := \frac{y}{\frac{a - t}{-t}}\\ \mathbf{if}\;t \leq -1.7602622053992855 \cdot 10^{+257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.584847870241093 \cdot 10^{+235}:\\ \;\;\;\;\frac{x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;t \leq -2.3730116082999515 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8477742541146235 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	34.0
Cost	844

\[\begin{array}{l} \mathbf{if}\;t \leq -1.5857366654332107 \cdot 10^{+61}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-121}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;t \leq 3.4526091493963727 \cdot 10^{+36}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 6
Error	32.4
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -2.3730116082999515 \cdot 10^{+86}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.4526091493963727 \cdot 10^{+36}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7
Error	35.6
Cost	328

\[\begin{array}{l} \mathbf{if}\;t \leq -2.3730116082999515 \cdot 10^{+86}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.4526091493963727 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8
Error	45.7
Cost	64

\[y \]

Reproduce

herbie shell --seed 2022228 
(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))))