Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A

Percentage Accurate: 98.5% → 98.5%

Time: 48.6s

Precision: binary64

Cost: 20160

Math

\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

↓

\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t + -1\right) \cdot \log a\right) - b}}{y} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))

↓

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (+ t -1.0) (log a))) b))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
}

↓

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + ((t + -1.0) * log(a))) - b))) / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    code = (x * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y
end function

↓

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    code = (x * exp((((y * log(z)) + ((t + (-1.0d0)) * log(a))) - b))) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.exp((((y * Math.log(z)) + ((t - 1.0) * Math.log(a))) - b))) / y;
}

↓

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.exp((((y * Math.log(z)) + ((t + -1.0) * Math.log(a))) - b))) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + ((t - 1.0) * math.log(a))) - b))) / y

↓

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + ((t + -1.0) * math.log(a))) - b))) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
end

↓

function code(x, y, z, t, a, b)
	return Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t + -1.0) * log(a))) - b))) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
end

↓

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + ((t + -1.0) * log(a))) - b))) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Target

Original	98.5%
Target	71.6%
Herbie	98.5%

\[\begin{array}{l} \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array} \]

Derivation

1. Initial program 98.4%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

2. Final simplification 98.4%

   \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \left(t + -1\right) \cdot \log a\right) - b}}{y} \]

Alternatives

Alternative 1
Accuracy	98.5%
Cost	20160

\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t + -1\right) \cdot \log a\right) - b}}{y} \]

Alternative 2
Accuracy	92.2%
Cost	33481

\[\begin{array}{l} t_1 := \left(t + -1\right) \cdot \log a\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+23} \lor \neg \left(t_1 \leq 5 \cdot 10^{+108}\right):\\ \;\;\;\;\frac{x \cdot e^{t_1 - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]

Alternative 3
Accuracy	89.1%
Cost	13769

\[\begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+57} \lor \neg \left(y \leq 3.1 \cdot 10^{+148}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 4
Accuracy	79.4%
Cost	13705

\[\begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+103} \lor \neg \left(t \leq 1.42 \cdot 10^{+65}\right):\\ \;\;\;\;\frac{\frac{x \cdot {a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y \cdot \left(a \cdot e^{b}\right)}\\ \end{array} \]

Alternative 5
Accuracy	79.5%
Cost	13704

\[\begin{array}{l} t_1 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-82}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+138}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Accuracy	73.1%
Cost	7308

\[\begin{array}{l} t_1 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-131}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+138}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	72.8%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+122} \lor \neg \left(t \leq 1.55 \cdot 10^{+65}\right):\\ \;\;\;\;\frac{\frac{x \cdot {a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 8
Accuracy	58.3%
Cost	6848

\[\frac{x}{a \cdot \left(y \cdot e^{b}\right)} \]

Alternative 9
Accuracy	44.2%
Cost	1348

\[\begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{-58}:\\ \;\;\;\;\frac{\left(\frac{x}{a} - b \cdot \frac{x}{a}\right) + \frac{x \cdot \left(b \cdot b\right)}{a}}{y}\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{b}}{a}}{y}\\ \end{array} \]

Alternative 10
Accuracy	39.0%
Cost	1028

\[\begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{\frac{x \cdot \left(a \cdot \left(b + -1\right)\right)}{-a \cdot a}}{y}\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(1 + b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{b}}{a}}{y}\\ \end{array} \]

Alternative 11
Accuracy	39.3%
Cost	836

\[\begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{b}}{a}}{y}\\ \end{array} \]

Alternative 12
Accuracy	38.3%
Cost	712

\[\begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+45}:\\ \;\;\;\;\frac{-b}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-80}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{b}}{a}}{y}\\ \end{array} \]

Alternative 13
Accuracy	39.3%
Cost	712

\[\begin{array}{l} \mathbf{if}\;b \leq -3.15 \cdot 10^{+44}:\\ \;\;\;\;-x \cdot \frac{\frac{b}{y}}{a}\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{b}}{a}}{y}\\ \end{array} \]

Alternative 14
Accuracy	39.1%
Cost	712

\[\begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{\left(-x\right) \cdot \frac{b}{a}}{y}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{b}}{a}}{y}\\ \end{array} \]

Alternative 15
Accuracy	34.8%
Cost	580

\[\begin{array}{l} \mathbf{if}\;b \leq 4.8 \cdot 10^{+118}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 16
Accuracy	35.0%
Cost	580

\[\begin{array}{l} \mathbf{if}\;b \leq 2.9 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \]

Alternative 17
Accuracy	35.1%
Cost	580

\[\begin{array}{l} \mathbf{if}\;b \leq 2.85 \cdot 10^{-80}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{b}}{a}}{y}\\ \end{array} \]

Alternative 18
Accuracy	30.9%
Cost	320

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

Reproduce

herbie shell --seed 2023263 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))