Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, H

Percentage Accurate: 95.3% → 97.5%

Time: 15.5s

Precision: binary64

Cost: 1988

• 27.4% of points produce a very large (infinite) output. You may want to add a precondition.

Math

\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

↓

\[\begin{array}{l} t_1 := \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (- x (/ y (* z 3.0))) (/ t (* y (* z 3.0))))))
   (if (<= t_1 5e+304) t_1 (+ x (/ (- y (/ t y)) (* z -3.0))))))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

↓

double code(double x, double y, double z, double t) {
	double t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	double tmp;
	if (t_1 <= 5e+304) {
		tmp = t_1;
	} else {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	}
	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 * 3.0d0))) + (t / ((z * 3.0d0) * y))
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 = (x - (y / (z * 3.0d0))) + (t / (y * (z * 3.0d0)))
    if (t_1 <= 5d+304) then
        tmp = t_1
    else
        tmp = x + ((y - (t / y)) / (z * (-3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

↓

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	double tmp;
	if (t_1 <= 5e+304) {
		tmp = t_1;
	} else {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))

↓

def code(x, y, z, t):
	t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)))
	tmp = 0
	if t_1 <= 5e+304:
		tmp = t_1
	else:
		tmp = x + ((y - (t / y)) / (z * -3.0))
	return tmp

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)))
end

↓

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(y * Float64(z * 3.0))))
	tmp = 0.0
	if (t_1 <= 5e+304)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(y - Float64(t / y)) / Float64(z * -3.0)));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
end

↓

function tmp_2 = code(x, y, z, t)
	t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	tmp = 0.0;
	if (t_1 <= 5e+304)
		tmp = t_1;
	else
		tmp = x + ((y - (t / y)) / (z * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+304], t$95$1, N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	95.3%
Target	95.8%
Herbie	97.5%

\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y} \]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y))) < 4.9999999999999997e304

   1. Initial program 98.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   if 4.9999999999999997e304 < (+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))

   1. Initial program 79.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Simplified 99.8%

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
      Step-by-step derivation

      [Start] 79.9%	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      associate-+l- [=>] 79.9%	\[ \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      sub-neg [=>] 79.9%	\[ \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      sub-neg [=>] 79.9%	\[ x + \left(-\color{blue}{\left(\frac{y}{z \cdot 3} + \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right) \]
      distribute-neg-in [=>] 79.9%	\[ x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) + \left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)} \]
      unsub-neg [=>] 79.9%	\[ x + \color{blue}{\left(\left(-\frac{y}{z \cdot 3}\right) - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      neg-mul-1 [=>] 79.9%	\[ x + \left(\color{blue}{-1 \cdot \frac{y}{z \cdot 3}} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      associate-*r/ [=>] 79.9%	\[ x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      associate-*l/ [<=] 79.9%	\[ x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - \left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right) \]
      distribute-neg-frac [=>] 79.9%	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right) \]
      neg-mul-1 [=>] 79.9%	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\right) \]
      times-frac [=>] 96.8%	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]
      distribute-lft-out-- [=>] 99.9%	\[ x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]
      *-commutative [=>] 99.9%	\[ x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]
      associate-/r* [=>] 99.8%	\[ x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]
      metadata-eval [=>] 99.8%	\[ x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Applied egg-rr 99.9%

      \[\leadsto x + \color{blue}{\frac{y - \frac{t}{y}}{z \cdot -3}} \]
      Step-by-step derivation

      [Start] 99.8%	\[ x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right) \]
      *-commutative [=>] 99.8%	\[ x + \color{blue}{\left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}} \]
      clear-num [=>] 99.8%	\[ x + \left(y - \frac{t}{y}\right) \cdot \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \]
      un-div-inv [=>] 99.8%	\[ x + \color{blue}{\frac{y - \frac{t}{y}}{\frac{z}{-0.3333333333333333}}} \]
      div-inv [=>] 99.9%	\[ x + \frac{y - \frac{t}{y}}{\color{blue}{z \cdot \frac{1}{-0.3333333333333333}}} \]
      metadata-eval [=>] 99.9%	\[ x + \frac{y - \frac{t}{y}}{z \cdot \color{blue}{-3}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	97.5%
Cost	1988

\[\begin{array}{l} t_1 := \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \end{array} \]

Alternative 2
Accuracy	96.4%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -7100000 \lor \neg \left(y \leq 0.035\right):\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \end{array} \]

Alternative 3
Accuracy	96.3%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -235000000 \lor \neg \left(y \leq 0.035\right):\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \end{array} \]

Alternative 4
Accuracy	97.0%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -7100000 \lor \neg \left(y \leq 2.75 \cdot 10^{-49}\right):\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \end{array} \]

Alternative 5
Accuracy	96.9%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -235000000 \lor \neg \left(y \leq 2.75 \cdot 10^{-49}\right):\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \left(\frac{1}{y} \cdot \frac{t}{z}\right)\\ \end{array} \]

Alternative 6
Accuracy	88.5%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+38} \lor \neg \left(y \leq 1.85 \cdot 10^{+42}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \end{array} \]

Alternative 7
Accuracy	89.1%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+38} \lor \neg \left(y \leq 1.22 \cdot 10^{+42}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{z \cdot \frac{y}{t}}\\ \end{array} \]

Alternative 8
Accuracy	89.7%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+40} \lor \neg \left(y \leq 3.9 \cdot 10^{+31}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot 0.3333333333333333}{y \cdot z}\\ \end{array} \]

Alternative 9
Accuracy	92.3%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+38} \lor \neg \left(y \leq 1.7 \cdot 10^{+31}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \end{array} \]

Alternative 10
Accuracy	92.1%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+38} \lor \neg \left(y \leq 3.2 \cdot 10^{+38}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{t \cdot -0.3333333333333333}{z}}{y}\\ \end{array} \]

Alternative 11
Accuracy	47.9%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+17} \lor \neg \left(y \leq 2.65 \cdot 10^{+19}\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Accuracy	48.0%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+20} \lor \neg \left(y \leq 8.6 \cdot 10^{+19}\right):\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Accuracy	48.0%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+14} \lor \neg \left(y \leq 3.1 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14
Accuracy	48.0%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+20}:\\ \;\;\;\;\frac{y}{\frac{z}{-0.3333333333333333}}\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \]

Alternative 15
Accuracy	64.0%
Cost	448

\[x + y \cdot \frac{-0.3333333333333333}{z} \]

Alternative 16
Accuracy	64.0%
Cost	448

\[x + \frac{y}{z \cdot -3} \]

Alternative 17
Accuracy	30.8%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023271 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))