exp neg sub

Percentage Accurate: 100.0% → 100.0%

Time: 3.6s

Alternatives: 4

Speedup: 1.0×

• 50.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ e^{-\left(1 - x \cdot x\right)} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (exp (- (- 1.0 (* x x)))))

C

double code(double x) {
	return exp(-(1.0 - (x * x)));
}

Fortran

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

Java

public static double code(double x) {
	return Math.exp(-(1.0 - (x * x)));
}

Python

def code(x):
	return math.exp(-(1.0 - (x * x)))

Julia

function code(x)
	return exp(Float64(-Float64(1.0 - Float64(x * x))))
end

MATLAB

function tmp = code(x)
	tmp = exp(-(1.0 - (x * x)));
end

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ e^{-\left(1 - x \cdot x\right)} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (exp (- (- 1.0 (* x x)))))

C

double code(double x) {
	return exp(-(1.0 - (x * x)));
}

Fortran

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

Java

public static double code(double x) {
	return Math.exp(-(1.0 - (x * x)));
}

Python

def code(x):
	return math.exp(-(1.0 - (x * x)))

Julia

function code(x)
	return exp(Float64(-Float64(1.0 - Float64(x * x))))
end

MATLAB

function tmp = code(x)
	tmp = exp(-(1.0 - (x * x)));
end

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ e^{x \cdot x + -1} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (exp (+ (* x x) -1.0)))

C

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

Fortran

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

Java

public static double code(double x) {
	return Math.exp(((x * x) + -1.0));
}

Python

def code(x):
	return math.exp(((x * x) + -1.0))

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[e^{-\left(1 - x \cdot x\right)} \]
2. Step-by-step derivation

   1. sqr-neg 100.0%

      \[\leadsto e^{-\left(1 - \color{blue}{\left(-x\right) \cdot \left(-x\right)}\right)} \]

   2. neg-sub0 100.0%

      \[\leadsto e^{\color{blue}{0 - \left(1 - \left(-x\right) \cdot \left(-x\right)\right)}} \]

   3. associate--r- 100.0%

      \[\leadsto e^{\color{blue}{\left(0 - 1\right) + \left(-x\right) \cdot \left(-x\right)}} \]

   4. metadata-eval 100.0%

      \[\leadsto e^{\color{blue}{-1} + \left(-x\right) \cdot \left(-x\right)} \]

   5. +-commutative 100.0%

      \[\leadsto e^{\color{blue}{\left(-x\right) \cdot \left(-x\right) + -1}} \]

   6. sqr-neg 100.0%

      \[\leadsto e^{\color{blue}{x \cdot x} + -1} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{e^{x \cdot x + -1}} \]
4. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto e^{x \cdot x + -1} \]
6. Add Preprocessing

Alternative 2: 62.8% accurate, 10.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;\frac{1}{e}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{x}{e}\\ \end{array} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (if (<= x 1.0) (/ 1.0 E) (* x (/ x E))))

C

double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = 1.0 / ((double) M_E);
	} else {
		tmp = x * (x / ((double) M_E));
	}
	return tmp;
}

Java

public static double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = 1.0 / Math.E;
	} else {
		tmp = x * (x / Math.E);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 1.0:
		tmp = 1.0 / math.e
	else:
		tmp = x * (x / math.e)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 1.0)
		tmp = Float64(1.0 / exp(1));
	else
		tmp = Float64(x * Float64(x / exp(1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 1.0)
		tmp = 1.0 / 2.71828182845904523536;
	else
		tmp = x * (x / 2.71828182845904523536);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 1.0], N[(1.0 / E), $MachinePrecision], N[(x * N[(x / E), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1

   1. Initial program 100.0%

      \[e^{-\left(1 - x \cdot x\right)} \]
   2. Step-by-step derivation

      1. sqr-neg 100.0%

         \[\leadsto e^{-\left(1 - \color{blue}{\left(-x\right) \cdot \left(-x\right)}\right)} \]

      2. neg-sub0 100.0%

         \[\leadsto e^{\color{blue}{0 - \left(1 - \left(-x\right) \cdot \left(-x\right)\right)}} \]

      3. associate--r- 100.0%

         \[\leadsto e^{\color{blue}{\left(0 - 1\right) + \left(-x\right) \cdot \left(-x\right)}} \]

      4. metadata-eval 100.0%

         \[\leadsto e^{\color{blue}{-1} + \left(-x\right) \cdot \left(-x\right)} \]

      5. +-commutative 100.0%

         \[\leadsto e^{\color{blue}{\left(-x\right) \cdot \left(-x\right) + -1}} \]

      6. sqr-neg 100.0%

         \[\leadsto e^{\color{blue}{x \cdot x} + -1} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{e^{x \cdot x + -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 86.6%

      \[\leadsto \color{blue}{e^{-1} + {x}^{2} \cdot e^{-1}} \]
   6. Step-by-step derivation

      1. distribute-rgt1-in 86.6%

         \[\leadsto \color{blue}{\left({x}^{2} + 1\right) \cdot e^{-1}} \]

      2. unpow2 86.6%

         \[\leadsto \left(\color{blue}{x \cdot x} + 1\right) \cdot e^{-1} \]

      3. fma-undefine 86.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, 1\right)} \cdot e^{-1} \]

      4. *-commutative 86.6%

         \[\leadsto \color{blue}{e^{-1} \cdot \mathsf{fma}\left(x, x, 1\right)} \]

      5. metadata-eval 86.6%

         \[\leadsto e^{\color{blue}{-1}} \cdot \mathsf{fma}\left(x, x, 1\right) \]

      6. rec-exp 86.6%

         \[\leadsto \color{blue}{\frac{1}{e^{1}}} \cdot \mathsf{fma}\left(x, x, 1\right) \]

      7. e-exp-1 86.6%

         \[\leadsto \frac{1}{\color{blue}{e}} \cdot \mathsf{fma}\left(x, x, 1\right) \]

      8. associate-*l/ 86.6%

         \[\leadsto \color{blue}{\frac{1 \cdot \mathsf{fma}\left(x, x, 1\right)}{e}} \]

      9. *-lft-identity 86.6%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, x, 1\right)}}{e} \]

   7. Simplified 86.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, x, 1\right)}{e}} \]

   8. Taylor expanded in x around 0 67.8%

      \[\leadsto \color{blue}{\frac{1}{e}} \]

   if 1 < x

   1. Initial program 100.0%

      \[e^{-\left(1 - x \cdot x\right)} \]
   2. Step-by-step derivation

      1. sqr-neg 100.0%

         \[\leadsto e^{-\left(1 - \color{blue}{\left(-x\right) \cdot \left(-x\right)}\right)} \]

      2. neg-sub0 100.0%

         \[\leadsto e^{\color{blue}{0 - \left(1 - \left(-x\right) \cdot \left(-x\right)\right)}} \]

      3. associate--r- 100.0%

         \[\leadsto e^{\color{blue}{\left(0 - 1\right) + \left(-x\right) \cdot \left(-x\right)}} \]

      4. metadata-eval 100.0%

         \[\leadsto e^{\color{blue}{-1} + \left(-x\right) \cdot \left(-x\right)} \]

      5. +-commutative 100.0%

         \[\leadsto e^{\color{blue}{\left(-x\right) \cdot \left(-x\right) + -1}} \]

      6. sqr-neg 100.0%

         \[\leadsto e^{\color{blue}{x \cdot x} + -1} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{e^{x \cdot x + -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 55.0%

      \[\leadsto \color{blue}{e^{-1} + {x}^{2} \cdot e^{-1}} \]
   6. Step-by-step derivation

      1. distribute-rgt1-in 55.0%

         \[\leadsto \color{blue}{\left({x}^{2} + 1\right) \cdot e^{-1}} \]

      2. unpow2 55.0%

         \[\leadsto \left(\color{blue}{x \cdot x} + 1\right) \cdot e^{-1} \]

      3. fma-undefine 55.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, 1\right)} \cdot e^{-1} \]

      4. *-commutative 55.0%

         \[\leadsto \color{blue}{e^{-1} \cdot \mathsf{fma}\left(x, x, 1\right)} \]

      5. metadata-eval 55.0%

         \[\leadsto e^{\color{blue}{-1}} \cdot \mathsf{fma}\left(x, x, 1\right) \]

      6. rec-exp 55.0%

         \[\leadsto \color{blue}{\frac{1}{e^{1}}} \cdot \mathsf{fma}\left(x, x, 1\right) \]

      7. e-exp-1 55.0%

         \[\leadsto \frac{1}{\color{blue}{e}} \cdot \mathsf{fma}\left(x, x, 1\right) \]

      8. associate-*l/ 55.0%

         \[\leadsto \color{blue}{\frac{1 \cdot \mathsf{fma}\left(x, x, 1\right)}{e}} \]

      9. *-lft-identity 55.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, x, 1\right)}}{e} \]

   7. Simplified 55.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, x, 1\right)}{e}} \]

   8. Taylor expanded in x around inf 55.0%

      \[\leadsto \color{blue}{\frac{{x}^{2}}{e}} \]
   9. Step-by-step derivation

      1. unpow2 55.0%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{e} \]

      2. associate-/l* 53.7%

         \[\leadsto \color{blue}{x \cdot \frac{x}{e}} \]

   10. Applied egg-rr 53.7%

       \[\leadsto \color{blue}{x \cdot \frac{x}{e}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;\frac{1}{e}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{x}{e}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.8% accurate, 10.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;\frac{1}{e}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot x}{e}\\ \end{array} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (if (<= x 1.0) (/ 1.0 E) (/ (* x x) E)))

C

double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = 1.0 / ((double) M_E);
	} else {
		tmp = (x * x) / ((double) M_E);
	}
	return tmp;
}

Java

public static double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = 1.0 / Math.E;
	} else {
		tmp = (x * x) / Math.E;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 1.0:
		tmp = 1.0 / math.e
	else:
		tmp = (x * x) / math.e
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 1.0)
		tmp = Float64(1.0 / exp(1));
	else
		tmp = Float64(Float64(x * x) / exp(1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 1.0)
		tmp = 1.0 / 2.71828182845904523536;
	else
		tmp = (x * x) / 2.71828182845904523536;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 1.0], N[(1.0 / E), $MachinePrecision], N[(N[(x * x), $MachinePrecision] / E), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1

   1. Initial program 100.0%

      \[e^{-\left(1 - x \cdot x\right)} \]
   2. Step-by-step derivation

      1. sqr-neg 100.0%

         \[\leadsto e^{-\left(1 - \color{blue}{\left(-x\right) \cdot \left(-x\right)}\right)} \]

      2. neg-sub0 100.0%

         \[\leadsto e^{\color{blue}{0 - \left(1 - \left(-x\right) \cdot \left(-x\right)\right)}} \]

      3. associate--r- 100.0%

         \[\leadsto e^{\color{blue}{\left(0 - 1\right) + \left(-x\right) \cdot \left(-x\right)}} \]

      4. metadata-eval 100.0%

         \[\leadsto e^{\color{blue}{-1} + \left(-x\right) \cdot \left(-x\right)} \]

      5. +-commutative 100.0%

         \[\leadsto e^{\color{blue}{\left(-x\right) \cdot \left(-x\right) + -1}} \]

      6. sqr-neg 100.0%

         \[\leadsto e^{\color{blue}{x \cdot x} + -1} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{e^{x \cdot x + -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 86.6%

      \[\leadsto \color{blue}{e^{-1} + {x}^{2} \cdot e^{-1}} \]
   6. Step-by-step derivation

      1. distribute-rgt1-in 86.6%

         \[\leadsto \color{blue}{\left({x}^{2} + 1\right) \cdot e^{-1}} \]

      2. unpow2 86.6%

         \[\leadsto \left(\color{blue}{x \cdot x} + 1\right) \cdot e^{-1} \]

      3. fma-undefine 86.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, 1\right)} \cdot e^{-1} \]

      4. *-commutative 86.6%

         \[\leadsto \color{blue}{e^{-1} \cdot \mathsf{fma}\left(x, x, 1\right)} \]

      5. metadata-eval 86.6%

         \[\leadsto e^{\color{blue}{-1}} \cdot \mathsf{fma}\left(x, x, 1\right) \]

      6. rec-exp 86.6%

         \[\leadsto \color{blue}{\frac{1}{e^{1}}} \cdot \mathsf{fma}\left(x, x, 1\right) \]

      7. e-exp-1 86.6%

         \[\leadsto \frac{1}{\color{blue}{e}} \cdot \mathsf{fma}\left(x, x, 1\right) \]

      8. associate-*l/ 86.6%

         \[\leadsto \color{blue}{\frac{1 \cdot \mathsf{fma}\left(x, x, 1\right)}{e}} \]

      9. *-lft-identity 86.6%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, x, 1\right)}}{e} \]

   7. Simplified 86.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, x, 1\right)}{e}} \]

   8. Taylor expanded in x around 0 67.8%

      \[\leadsto \color{blue}{\frac{1}{e}} \]

   if 1 < x

   1. Initial program 100.0%

      \[e^{-\left(1 - x \cdot x\right)} \]
   2. Step-by-step derivation

      1. sqr-neg 100.0%

         \[\leadsto e^{-\left(1 - \color{blue}{\left(-x\right) \cdot \left(-x\right)}\right)} \]

      2. neg-sub0 100.0%

         \[\leadsto e^{\color{blue}{0 - \left(1 - \left(-x\right) \cdot \left(-x\right)\right)}} \]

      3. associate--r- 100.0%

         \[\leadsto e^{\color{blue}{\left(0 - 1\right) + \left(-x\right) \cdot \left(-x\right)}} \]

      4. metadata-eval 100.0%

         \[\leadsto e^{\color{blue}{-1} + \left(-x\right) \cdot \left(-x\right)} \]

      5. +-commutative 100.0%

         \[\leadsto e^{\color{blue}{\left(-x\right) \cdot \left(-x\right) + -1}} \]

      6. sqr-neg 100.0%

         \[\leadsto e^{\color{blue}{x \cdot x} + -1} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{e^{x \cdot x + -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 55.0%

      \[\leadsto \color{blue}{e^{-1} + {x}^{2} \cdot e^{-1}} \]
   6. Step-by-step derivation

      1. distribute-rgt1-in 55.0%

         \[\leadsto \color{blue}{\left({x}^{2} + 1\right) \cdot e^{-1}} \]

      2. unpow2 55.0%

         \[\leadsto \left(\color{blue}{x \cdot x} + 1\right) \cdot e^{-1} \]

      3. fma-undefine 55.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, 1\right)} \cdot e^{-1} \]

      4. *-commutative 55.0%

         \[\leadsto \color{blue}{e^{-1} \cdot \mathsf{fma}\left(x, x, 1\right)} \]

      5. metadata-eval 55.0%

         \[\leadsto e^{\color{blue}{-1}} \cdot \mathsf{fma}\left(x, x, 1\right) \]

      6. rec-exp 55.0%

         \[\leadsto \color{blue}{\frac{1}{e^{1}}} \cdot \mathsf{fma}\left(x, x, 1\right) \]

      7. e-exp-1 55.0%

         \[\leadsto \frac{1}{\color{blue}{e}} \cdot \mathsf{fma}\left(x, x, 1\right) \]

      8. associate-*l/ 55.0%

         \[\leadsto \color{blue}{\frac{1 \cdot \mathsf{fma}\left(x, x, 1\right)}{e}} \]

      9. *-lft-identity 55.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, x, 1\right)}}{e} \]

   7. Simplified 55.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, x, 1\right)}{e}} \]

   8. Taylor expanded in x around inf 55.0%

      \[\leadsto \color{blue}{\frac{{x}^{2}}{e}} \]
   9. Step-by-step derivation

      1. unpow2 55.0%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{e} \]

      2. associate-/l* 53.7%

         \[\leadsto \color{blue}{x \cdot \frac{x}{e}} \]

   10. Applied egg-rr 53.7%

       \[\leadsto \color{blue}{x \cdot \frac{x}{e}} \]
   11. Step-by-step derivation

       1. *-commutative 53.7%

          \[\leadsto \color{blue}{\frac{x}{e} \cdot x} \]

       2. frac-2neg 53.7%

          \[\leadsto \color{blue}{\frac{-x}{-e}} \cdot x \]

       3. associate-*l/ 55.0%

          \[\leadsto \color{blue}{\frac{\left(-x\right) \cdot x}{-e}} \]

   12. Applied egg-rr 55.0%

       \[\leadsto \color{blue}{\frac{\left(-x\right) \cdot x}{-e}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;\frac{1}{e}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot x}{e}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.3% accurate, 35.3× speedup

Math

\[\begin{array}{l} \\ \frac{1}{e} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ 1.0 E))

C

double code(double x) {
	return 1.0 / ((double) M_E);
}

Java

public static double code(double x) {
	return 1.0 / Math.E;
}

Python

def code(x):
	return 1.0 / math.e

Julia

function code(x)
	return Float64(1.0 / exp(1))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 / 2.71828182845904523536;
end

Wolfram

code[x_] := N[(1.0 / E), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[e^{-\left(1 - x \cdot x\right)} \]
2. Step-by-step derivation

   1. sqr-neg 100.0%

      \[\leadsto e^{-\left(1 - \color{blue}{\left(-x\right) \cdot \left(-x\right)}\right)} \]

   2. neg-sub0 100.0%

      \[\leadsto e^{\color{blue}{0 - \left(1 - \left(-x\right) \cdot \left(-x\right)\right)}} \]

   3. associate--r- 100.0%

      \[\leadsto e^{\color{blue}{\left(0 - 1\right) + \left(-x\right) \cdot \left(-x\right)}} \]

   4. metadata-eval 100.0%

      \[\leadsto e^{\color{blue}{-1} + \left(-x\right) \cdot \left(-x\right)} \]

   5. +-commutative 100.0%

      \[\leadsto e^{\color{blue}{\left(-x\right) \cdot \left(-x\right) + -1}} \]

   6. sqr-neg 100.0%

      \[\leadsto e^{\color{blue}{x \cdot x} + -1} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{e^{x \cdot x + -1}} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 78.6%

   \[\leadsto \color{blue}{e^{-1} + {x}^{2} \cdot e^{-1}} \]
6. Step-by-step derivation

   1. distribute-rgt1-in 78.6%

      \[\leadsto \color{blue}{\left({x}^{2} + 1\right) \cdot e^{-1}} \]

   2. unpow2 78.6%

      \[\leadsto \left(\color{blue}{x \cdot x} + 1\right) \cdot e^{-1} \]

   3. fma-undefine 78.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, 1\right)} \cdot e^{-1} \]

   4. *-commutative 78.6%

      \[\leadsto \color{blue}{e^{-1} \cdot \mathsf{fma}\left(x, x, 1\right)} \]

   5. metadata-eval 78.6%

      \[\leadsto e^{\color{blue}{-1}} \cdot \mathsf{fma}\left(x, x, 1\right) \]

   6. rec-exp 78.6%

      \[\leadsto \color{blue}{\frac{1}{e^{1}}} \cdot \mathsf{fma}\left(x, x, 1\right) \]

   7. e-exp-1 78.6%

      \[\leadsto \frac{1}{\color{blue}{e}} \cdot \mathsf{fma}\left(x, x, 1\right) \]

   8. associate-*l/ 78.6%

      \[\leadsto \color{blue}{\frac{1 \cdot \mathsf{fma}\left(x, x, 1\right)}{e}} \]

   9. *-lft-identity 78.6%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, x, 1\right)}}{e} \]

7. Simplified 78.6%

   \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, x, 1\right)}{e}} \]

8. Taylor expanded in x around 0 51.4%

   \[\leadsto \color{blue}{\frac{1}{e}} \]

9. Final simplification 51.4%

   \[\leadsto \frac{1}{e} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024047 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1.0 (* x x)))))