Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D

Average Error: 0.1 → 0.1

Time: 3.8s

Precision: binary64

Cost: 704

Math

\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]

↓

\[3 - \left(x \cdot 12 - \left(x \cdot x\right) \cdot 9\right) \]

FPCore

(FPCore (x) :precision binary64 (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))

↓

(FPCore (x) :precision binary64 (- 3.0 (- (* x 12.0) (* (* x x) 9.0))))

C

double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

↓

double code(double x) {
	return 3.0 - ((x * 12.0) - ((x * x) * 9.0));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 * ((((x * 3.0d0) * x) - (x * 4.0d0)) + 1.0d0)
end function

↓

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 - ((x * 12.0d0) - ((x * x) * 9.0d0))
end function

Java

public static double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

↓

public static double code(double x) {
	return 3.0 - ((x * 12.0) - ((x * x) * 9.0));
}

Python

def code(x):
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0)

↓

def code(x):
	return 3.0 - ((x * 12.0) - ((x * x) * 9.0))

Julia

function code(x)
	return Float64(3.0 * Float64(Float64(Float64(Float64(x * 3.0) * x) - Float64(x * 4.0)) + 1.0))
end

↓

function code(x)
	return Float64(3.0 - Float64(Float64(x * 12.0) - Float64(Float64(x * x) * 9.0)))
end

MATLAB

function tmp = code(x)
	tmp = 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
end

↓

function tmp = code(x)
	tmp = 3.0 - ((x * 12.0) - ((x * x) * 9.0));
end

Wolfram

code[x_] := N[(3.0 * N[(N[(N[(N[(x * 3.0), $MachinePrecision] * x), $MachinePrecision] - N[(x * 4.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]

↓

code[x_] := N[(3.0 - N[(N[(x * 12.0), $MachinePrecision] - N[(N[(x * x), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	0.1
Target	0.1
Herbie	0.1

\[3 + \left(\left(9 \cdot x\right) \cdot x - 12 \cdot x\right) \]

Derivation

1. Initial program 0.1

   \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]

2. Simplified 0.1

   \[\leadsto \color{blue}{3 - \left(x \cdot 12 - \left(x \cdot x\right) \cdot 9\right)} \]
   Proof

   [Start] 0.1	\[ 3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   rational_best_oopsla_all_46_json_45_simplify-11 [=>] 0.1	\[ 3 \cdot \color{blue}{\left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) - -1\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-87 [=>] 0.1	\[ \color{blue}{\left(-3\right) \cdot \left(-1 - \left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right)\right)} \]
   metadata-eval [=>] 0.1	\[ \color{blue}{-3} \cdot \left(-1 - \left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right)\right) \]
   metadata-eval [<=] 0.1	\[ \color{blue}{\left(3 \cdot -1\right)} \cdot \left(-1 - \left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right)\right) \]
   rational_best_oopsla_all_46_json_45_simplify-13 [=>] 0.1	\[ \color{blue}{-1 \cdot \left(3 \cdot -1\right) - \left(3 \cdot -1\right) \cdot \left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right)} \]
   metadata-eval [=>] 0.1	\[ -1 \cdot \color{blue}{-3} - \left(3 \cdot -1\right) \cdot \left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) \]
   metadata-eval [=>] 0.1	\[ \color{blue}{3} - \left(3 \cdot -1\right) \cdot \left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) \]
   rational_best_oopsla_all_46_json_45_simplify-87 [=>] 0.1	\[ 3 - \color{blue}{\left(-3 \cdot -1\right) \cdot \left(x \cdot 4 - \left(x \cdot 3\right) \cdot x\right)} \]
   metadata-eval [=>] 0.1	\[ 3 - \left(-\color{blue}{-3}\right) \cdot \left(x \cdot 4 - \left(x \cdot 3\right) \cdot x\right) \]
   metadata-eval [=>] 0.1	\[ 3 - \color{blue}{3} \cdot \left(x \cdot 4 - \left(x \cdot 3\right) \cdot x\right) \]
   rational_best_oopsla_all_46_json_45_simplify-13 [=>] 0.1	\[ 3 - \color{blue}{\left(\left(x \cdot 4\right) \cdot 3 - 3 \cdot \left(\left(x \cdot 3\right) \cdot x\right)\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-74 [<=] 0.1	\[ 3 - \left(\color{blue}{3 \cdot \left(x \cdot 4\right)} - 3 \cdot \left(\left(x \cdot 3\right) \cdot x\right)\right) \]
   rational_best_oopsla_all_46_json_45_simplify-7 [=>] 0.1	\[ 3 - \left(\color{blue}{x \cdot \left(3 \cdot 4\right)} - 3 \cdot \left(\left(x \cdot 3\right) \cdot x\right)\right) \]
   metadata-eval [=>] 0.1	\[ 3 - \left(x \cdot \color{blue}{12} - 3 \cdot \left(\left(x \cdot 3\right) \cdot x\right)\right) \]
   rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.1	\[ 3 - \left(x \cdot 12 - 3 \cdot \color{blue}{\left(x \cdot \left(x \cdot 3\right)\right)}\right) \]
   rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.1	\[ 3 - \left(x \cdot 12 - 3 \cdot \left(x \cdot \color{blue}{\left(3 \cdot x\right)}\right)\right) \]
   rational_best_oopsla_all_46_json_45_simplify-7 [=>] 0.1	\[ 3 - \left(x \cdot 12 - 3 \cdot \color{blue}{\left(3 \cdot \left(x \cdot x\right)\right)}\right) \]
   rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.1	\[ 3 - \left(x \cdot 12 - 3 \cdot \color{blue}{\left(\left(x \cdot x\right) \cdot 3\right)}\right) \]
   rational_best_oopsla_all_46_json_45_simplify-7 [=>] 0.1	\[ 3 - \left(x \cdot 12 - \color{blue}{\left(x \cdot x\right) \cdot \left(3 \cdot 3\right)}\right) \]
   metadata-eval [=>] 0.1	\[ 3 - \left(x \cdot 12 - \left(x \cdot x\right) \cdot \color{blue}{9}\right) \]

3. Final simplification 0.1

   \[\leadsto 3 - \left(x \cdot 12 - \left(x \cdot x\right) \cdot 9\right) \]

Alternatives

Alternative 1
Error	0.1
Cost	576

\[x \cdot \left(9 \cdot x + -12\right) - -3 \]

Alternative 2
Error	2.0
Cost	448

\[9 \cdot \left(x \cdot x\right) - -3 \]

Alternative 3
Error	20.8
Cost	320

\[3 - x \cdot 12 \]

Alternative 4
Error	21.0
Cost	64

\[3 \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :herbie-target
  (+ 3.0 (- (* (* 9.0 x) x) (* 12.0 x)))

  (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))