Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B

Average Error: 7.3 → 1.4

Time: 2.0min

Precision: binary64

Cost: 1608

Math

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

↓

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+106}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z - y}\\ \mathbf{elif}\;t_1 \leq -4 \cdot 10^{-145}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z - y}}{z - t}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (<= t_1 -1e+106)
     (/ (/ x (- z t)) (- z y))
     (if (<= t_1 -4e-145) (/ x t_1) (/ (/ x (- z y)) (- z t))))))

C

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

↓

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -1e+106) {
		tmp = (x / (z - t)) / (z - y);
	} else if (t_1 <= -4e-145) {
		tmp = x / t_1;
	} else {
		tmp = (x / (z - y)) / (z - t);
	}
	return tmp;
}

Fortran

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

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if (t_1 <= (-1d+106)) then
        tmp = (x / (z - t)) / (z - y)
    else if (t_1 <= (-4d-145)) then
        tmp = x / t_1
    else
        tmp = (x / (z - y)) / (z - t)
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -1e+106) {
		tmp = (x / (z - t)) / (z - y);
	} else if (t_1 <= -4e-145) {
		tmp = x / t_1;
	} else {
		tmp = (x / (z - y)) / (z - t);
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= -1e+106:
		tmp = (x / (z - t)) / (z - y)
	elif t_1 <= -4e-145:
		tmp = x / t_1
	else:
		tmp = (x / (z - y)) / (z - t)
	return tmp

Julia

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

↓

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= -1e+106)
		tmp = Float64(Float64(x / Float64(z - t)) / Float64(z - y));
	elseif (t_1 <= -4e-145)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(x / Float64(z - y)) / Float64(z - t));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -1e+106)
		tmp = (x / (z - t)) / (z - y);
	elseif (t_1 <= -4e-145)
		tmp = x / t_1;
	else
		tmp = (x / (z - y)) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+106], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -4e-145], N[(x / t$95$1), $MachinePrecision], N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	7.3
Target	7.9
Herbie	1.4

\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -1.00000000000000009e106

   1. Initial program 9.0

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

   2. Simplified 1.4

      \[\leadsto \color{blue}{\frac{\frac{x}{z - t}}{z - y}} \]
      Proof

   if -1.00000000000000009e106 < (*.f64 (-.f64 y z) (-.f64 t z)) < -3.99999999999999966e-145

   1. Initial program 0.3

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

   if -3.99999999999999966e-145 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 7.8

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

   2. Applied egg-rr 1.6

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

Alternatives

Alternative 1
Error	4.2
Cost	1608

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ t_2 := \frac{x}{z - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2 \cdot \frac{-1}{y}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \frac{1}{z}\\ \end{array} \]

Alternative 2
Error	1.5
Cost	1608

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ t_2 := \frac{\frac{x}{z - t}}{z - y}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	12.7
Cost	1368

\[\begin{array}{l} t_1 := \frac{x}{z - t}\\ t_2 := t_1 \cdot \frac{-1}{y}\\ \mathbf{if}\;y \leq -310000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-69}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-87}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-72}:\\ \;\;\;\;\frac{t_1}{z}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+218}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	14.5
Cost	1108

\[\begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-69}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot z}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \end{array} \]

Alternative 5
Error	23.0
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+113}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	23.0
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.76 \cdot 10^{+111}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	23.2
Cost	912

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-62}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+110}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	19.1
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-148}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+110}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 9
Error	16.7
Cost	844

\[\begin{array}{l} t_1 := \frac{x}{\left(z - t\right) \cdot z}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 10
Error	14.5
Cost	844

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z - y}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	19.1
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 12
Error	14.4
Cost	712

\[\begin{array}{l} t_1 := \frac{\frac{x}{z - t}}{z}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	25.4
Cost	584

\[\begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	24.9
Cost	584

\[\begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	22.5
Cost	584

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	40.1
Cost	320

\[\frac{x}{y \cdot t} \]

Reproduce

herbie shell --seed 2023033 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :herbie-target
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

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