Linear.Quaternion:$ctanh from linear-1.19.1.3

Average Error: 2.7 → 0.3

Time: 4.8s

Precision: binary64

Math

\[\frac{x \cdot \frac{\sin y}{y}}{z} \]

↓

\[\begin{array}{l} t_0 := \frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{if}\;x \leq -1.7564181332187953 \cdot 10^{+74}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.0764093160980347 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (/ (sin y) y)) z))

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x (/ (sin y) y)) z)))
   (if (<= x -1.7564181332187953e+74)
     t_0
     (if (<= x 1.0764093160980347e+23) (/ x (* z (/ y (sin y)))) t_0))))

C

double code(double x, double y, double z) {
	return (x * (sin(y) / y)) / z;
}

↓

double code(double x, double y, double z) {
	double t_0 = (x * (sin(y) / y)) / z;
	double tmp;
	if (x <= -1.7564181332187953e+74) {
		tmp = t_0;
	} else if (x <= 1.0764093160980347e+23) {
		tmp = x / (z * (y / sin(y)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (sin(y) / y)) / z
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * (sin(y) / y)) / z
    if (x <= (-1.7564181332187953d+74)) then
        tmp = t_0
    else if (x <= 1.0764093160980347d+23) then
        tmp = x / (z * (y / sin(y)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	return (x * (Math.sin(y) / y)) / z;
}

↓

public static double code(double x, double y, double z) {
	double t_0 = (x * (Math.sin(y) / y)) / z;
	double tmp;
	if (x <= -1.7564181332187953e+74) {
		tmp = t_0;
	} else if (x <= 1.0764093160980347e+23) {
		tmp = x / (z * (y / Math.sin(y)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	return (x * (math.sin(y) / y)) / z

↓

def code(x, y, z):
	t_0 = (x * (math.sin(y) / y)) / z
	tmp = 0
	if x <= -1.7564181332187953e+74:
		tmp = t_0
	elif x <= 1.0764093160980347e+23:
		tmp = x / (z * (y / math.sin(y)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(sin(y) / y)) / z)
end

↓

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(sin(y) / y)) / z)
	tmp = 0.0
	if (x <= -1.7564181332187953e+74)
		tmp = t_0;
	elseif (x <= 1.0764093160980347e+23)
		tmp = Float64(x / Float64(z * Float64(y / sin(y))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (sin(y) / y)) / z;
end

↓

function tmp_2 = code(x, y, z)
	t_0 = (x * (sin(y) / y)) / z;
	tmp = 0.0;
	if (x <= -1.7564181332187953e+74)
		tmp = t_0;
	elseif (x <= 1.0764093160980347e+23)
		tmp = x / (z * (y / sin(y)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

↓

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[x, -1.7564181332187953e+74], t$95$0, If[LessEqual[x, 1.0764093160980347e+23], N[(x / N[(z * N[(y / N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Target

Original	2.7
Target	0.3
Herbie	0.3

\[\begin{array}{l} \mathbf{if}\;z < -4.2173720203427147 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if x < -1.7564181332187953e74 or 1.0764093160980347e23 < x

   1. Initial program 0.2

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]

   if -1.7564181332187953e74 < x < 1.0764093160980347e23

   1. Initial program 4.2

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]

   2. Applied egg-rr 0.3

      \[\leadsto \color{blue}{\frac{x}{z \cdot \frac{y}{\sin y}} \cdot 1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7564181332187953 \cdot 10^{+74}:\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{elif}\;x \leq 1.0764093160980347 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \end{array} \]

Reproduce

herbie shell --seed 2022210 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< z -4.2173720203427147e-29) (/ (* x (/ 1.0 (/ y (sin y)))) z) (if (< z 4.446702369113811e+64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1.0 (/ y (sin y)))) z)))

  (/ (* x (/ (sin y) y)) z))