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

Average Error: 0.1 → 0.1

Time: 8.0s

Precision: binary64

Cost: 832

Math

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

↓

\[3 + \left(\left(x \cdot 3\right) \cdot -4 + 9 \cdot \left(x \cdot x\right)\right) \]

FPCore

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

↓

(FPCore (x) :precision binary64 (+ 3.0 (+ (* (* x 3.0) -4.0) (* 9.0 (* x x)))))

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 * 3.0) * -4.0) + (9.0 * (x * x)));
}

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 * 3.0d0) * (-4.0d0)) + (9.0d0 * (x * x)))
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 * 3.0) * -4.0) + (9.0 * (x * x)));
}

Python

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

↓

def code(x):
	return 3.0 + (((x * 3.0) * -4.0) + (9.0 * (x * x)))

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(Float64(x * 3.0) * -4.0) + Float64(9.0 * Float64(x * x))))
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 * 3.0) * -4.0) + (9.0 * (x * x)));
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[(N[(x * 3.0), $MachinePrecision] * -4.0), $MachinePrecision] + N[(9.0 * N[(x * x), $MachinePrecision]), $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. Applied egg-rr 0.1

   \[\leadsto \color{blue}{3 \cdot \left(x \cdot \mathsf{fma}\left(x, 3, -4\right)\right) + 3} \]

3. Taylor expanded in x around 0 0.1

   \[\leadsto 3 \cdot \left(x \cdot \color{blue}{\left(3 \cdot x - 4\right)}\right) + 3 \]

4. Applied egg-rr 0.1

   \[\leadsto \color{blue}{\left(9 \cdot \left(x \cdot x\right) + \left(3 \cdot x\right) \cdot -4\right)} + 3 \]

5. Final simplification 0.1

   \[\leadsto 3 + \left(\left(x \cdot 3\right) \cdot -4 + 9 \cdot \left(x \cdot x\right)\right) \]

Alternatives

Alternative 1
Error	1.1
Cost	712

\[\begin{array}{l} t_0 := x \cdot \left(9 \cdot x + -12\right)\\ \mathbf{if}\;x \leq -12.228803319296599:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.002745088229694357:\\ \;\;\;\;3 + x \cdot -12\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	0.1
Cost	704

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

Alternative 3
Error	2.1
Cost	584

\[\begin{array}{l} t_0 := 9 \cdot \left(x \cdot x\right)\\ \mathbf{if}\;x \leq -12.228803319296599:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.615455569823281:\\ \;\;\;\;3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	1.5
Cost	584

\[\begin{array}{l} t_0 := 9 \cdot \left(x \cdot x\right)\\ \mathbf{if}\;x \leq -12.228803319296599:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.002745088229694357:\\ \;\;\;\;3 + x \cdot -12\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	1.5
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -12.228803319296599:\\ \;\;\;\;x \cdot \left(9 \cdot x\right)\\ \mathbf{elif}\;x \leq 0.002745088229694357:\\ \;\;\;\;3 + x \cdot -12\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot x\right)\\ \end{array} \]

Alternative 6
Error	20.7
Cost	64

\[3 \]

Reproduce

herbie shell --seed 2022310 
(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)))