fma_test2

Percentage Accurate: 33.9% → 99.6%

Time: 13.2s

Alternatives: 4

Speedup: 0.6×

Specification

\[1.9 \leq t \land t \leq 2.1\]

Math

\[\begin{array}{l} \\ 1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308} \end{array} \]

FPCore

(FPCore (t) :precision binary64 (- (* 1.7e+308 t) 1.7e+308))

C

double code(double t) {
	return (1.7e+308 * t) - 1.7e+308;
}

Fortran

real(8) function code(t)
    real(8), intent (in) :: t
    code = (1.7d+308 * t) - 1.7d+308
end function

Java

public static double code(double t) {
	return (1.7e+308 * t) - 1.7e+308;
}

Python

def code(t):
	return (1.7e+308 * t) - 1.7e+308

Julia

function code(t)
	return Float64(Float64(1.7e+308 * t) - 1.7e+308)
end

MATLAB

function tmp = code(t)
	tmp = (1.7e+308 * t) - 1.7e+308;
end

Wolfram

code[t_] := N[(N[(1.7e+308 * t), $MachinePrecision] - 1.7e+308), $MachinePrecision]

Initial Program: 33.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308} \end{array} \]

FPCore

(FPCore (t) :precision binary64 (- (* 1.7e+308 t) 1.7e+308))

C

double code(double t) {
	return (1.7e+308 * t) - 1.7e+308;
}

Fortran

real(8) function code(t)
    real(8), intent (in) :: t
    code = (1.7d+308 * t) - 1.7d+308
end function

Java

public static double code(double t) {
	return (1.7e+308 * t) - 1.7e+308;
}

Python

def code(t):
	return (1.7e+308 * t) - 1.7e+308

Julia

function code(t)
	return Float64(Float64(1.7e+308 * t) - 1.7e+308)
end

MATLAB

function tmp = code(t)
	tmp = (1.7e+308 * t) - 1.7e+308;
end

Wolfram

code[t_] := N[(N[(1.7e+308 * t), $MachinePrecision] - 1.7e+308), $MachinePrecision]

Alternative 1: 99.6% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right) \end{array} \]

FPCore

(FPCore (t) :precision binary64 (fma 1.7e+308 t -1.7e+308))

C

double code(double t) {
	return fma(1.7e+308, t, -1.7e+308);
}

Julia

function code(t)
	return fma(1.7e+308, t, -1.7e+308)
end

Wolfram

code[t_] := N[(1.7e+308 * t + -1.7e+308), $MachinePrecision]

Derivation

1. Initial program 36.7%

   \[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308} \]
2. Step-by-step derivation

   1. fma-neg 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)} \]

   2. metadata-eval 99.6%

      \[\leadsto \mathsf{fma}\left(1.7 \cdot 10^{+308}, t, \color{blue}{-1.7 \cdot 10^{+308}}\right) \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)} \]
4. Add Preprocessing

5. Final simplification 99.6%

   \[\leadsto \mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right) \]
6. Add Preprocessing

Alternative 2: 35.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.03:\\ \;\;\;\;1.7 \cdot 10^{+308}\\ \mathbf{else}:\\ \;\;\;\;1.7 \cdot 10^{+308} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (t) :precision binary64 (if (<= t 2.03) 1.7e+308 (* 1.7e+308 t)))

C

double code(double t) {
	double tmp;
	if (t <= 2.03) {
		tmp = 1.7e+308;
	} else {
		tmp = 1.7e+308 * t;
	}
	return tmp;
}

Fortran

real(8) function code(t)
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 2.03d0) then
        tmp = 1.7d+308
    else
        tmp = 1.7d+308 * t
    end if
    code = tmp
end function

Java

public static double code(double t) {
	double tmp;
	if (t <= 2.03) {
		tmp = 1.7e+308;
	} else {
		tmp = 1.7e+308 * t;
	}
	return tmp;
}

Python

def code(t):
	tmp = 0
	if t <= 2.03:
		tmp = 1.7e+308
	else:
		tmp = 1.7e+308 * t
	return tmp

Julia

function code(t)
	tmp = 0.0
	if (t <= 2.03)
		tmp = 1.7e+308;
	else
		tmp = Float64(1.7e+308 * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(t)
	tmp = 0.0;
	if (t <= 2.03)
		tmp = 1.7e+308;
	else
		tmp = 1.7e+308 * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[t_] := If[LessEqual[t, 2.03], 1.7e+308, N[(1.7e+308 * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.0299999999999998

   1. Initial program 22.7%

      \[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. fma-neg 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)} \]

      2. metadata-eval 99.5%

         \[\leadsto \mathsf{fma}\left(1.7 \cdot 10^{+308}, t, \color{blue}{-1.7 \cdot 10^{+308}}\right) \]

      3. add-cube-cbrt 97.7%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}} \]

      4. pow2 97.7%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{2}} \cdot \sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)} \]

   4. Applied egg-rr 97.7%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{2} \cdot \sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}} \]
   5. Step-by-step derivation

      1. pow-plus 97.7%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{\left(2 + 1\right)}} \]

      2. metadata-eval 97.7%

         \[\leadsto {\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{\color{blue}{3}} \]

      3. sqr-pow 97.6%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{\left(\frac{3}{2}\right)}} \]

      4. pow-prod-down 97.6%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{\left(\frac{3}{2}\right)}} \]

      5. unpow2 97.6%

         \[\leadsto {\color{blue}{\left({\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{2}\right)}}^{\left(\frac{3}{2}\right)} \]

      6. add-cube-cbrt 96.6%

         \[\leadsto {\color{blue}{\left(\left(\sqrt[3]{{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{2}} \cdot \sqrt[3]{{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{2}}\right) \cdot \sqrt[3]{{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{2}}\right)}}^{\left(\frac{3}{2}\right)} \]

      7. pow3 96.6%

         \[\leadsto {\color{blue}{\left({\left(\sqrt[3]{{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{2}}\right)}^{3}\right)}}^{\left(\frac{3}{2}\right)} \]

      8. pow-pow 96.6%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{2}}\right)}^{\left(3 \cdot \frac{3}{2}\right)}} \]

      9. unpow2 96.6%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}}}\right)}^{\left(3 \cdot \frac{3}{2}\right)} \]

      10. cbrt-prod 96.3%

          \[\leadsto {\color{blue}{\left(\sqrt[3]{\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}} \cdot \sqrt[3]{\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}}\right)}}^{\left(3 \cdot \frac{3}{2}\right)} \]

      11. pow2 96.3%

          \[\leadsto {\color{blue}{\left({\left(\sqrt[3]{\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}}\right)}^{2}\right)}}^{\left(3 \cdot \frac{3}{2}\right)} \]

      12. metadata-eval 96.3%

          \[\leadsto {\left({\left(\sqrt[3]{\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}}\right)}^{2}\right)}^{\left(3 \cdot \color{blue}{1.5}\right)} \]

      13. metadata-eval 96.3%

          \[\leadsto {\left({\left(\sqrt[3]{\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}}\right)}^{2}\right)}^{\color{blue}{4.5}} \]

   6. Applied egg-rr 96.3%

      \[\leadsto \color{blue}{{\left({\left(\sqrt[3]{\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}}\right)}^{2}\right)}^{4.5}} \]
   7. Step-by-step derivation

      1. fma-def 22.7%

         \[\leadsto {\left({\left(\sqrt[3]{\sqrt[3]{\color{blue}{1.7 \cdot 10^{+308} \cdot t + -1.7 \cdot 10^{+308}}}}\right)}^{2}\right)}^{4.5} \]

      2. *-commutative 22.7%

         \[\leadsto {\left({\left(\sqrt[3]{\sqrt[3]{\color{blue}{t \cdot 1.7 \cdot 10^{+308}} + -1.7 \cdot 10^{+308}}}\right)}^{2}\right)}^{4.5} \]

      3. fma-udef 96.3%

         \[\leadsto {\left({\left(\sqrt[3]{\sqrt[3]{\color{blue}{\mathsf{fma}\left(t, 1.7 \cdot 10^{+308}, -1.7 \cdot 10^{+308}\right)}}}\right)}^{2}\right)}^{4.5} \]

   8. Simplified 96.3%

      \[\leadsto \color{blue}{{\left({\left(\sqrt[3]{\sqrt[3]{\mathsf{fma}\left(t, 1.7 \cdot 10^{+308}, -1.7 \cdot 10^{+308}\right)}}\right)}^{2}\right)}^{4.5}} \]

   9. Taylor expanded in t around 0 25.0%

      \[\leadsto \color{blue}{1.7 \cdot 10^{+308}} \]

   if 2.0299999999999998 < t

   1. Initial program 78.6%

      \[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 78.6%

      \[\leadsto \color{blue}{1.7 \cdot 10^{+308} \cdot t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.03:\\ \;\;\;\;1.7 \cdot 10^{+308}\\ \mathbf{else}:\\ \;\;\;\;1.7 \cdot 10^{+308} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 0.0% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ -1.7 \cdot 10^{+308} \end{array} \]

FPCore

(FPCore (t) :precision binary64 -1.7e+308)

C

double code(double t) {
	return -1.7e+308;
}

Fortran

real(8) function code(t)
    real(8), intent (in) :: t
    code = -1.7d+308
end function

Java

public static double code(double t) {
	return -1.7e+308;
}

Python

def code(t):
	return -1.7e+308

Julia

function code(t)
	return -1.7e+308
end

MATLAB

function tmp = code(t)
	tmp = -1.7e+308;
end

Wolfram

code[t_] := -1.7e+308

Derivation

1. Initial program 36.7%

   \[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308} \]
2. Add Preprocessing

3. Taylor expanded in t around 0 0.0%

   \[\leadsto \color{blue}{-1.7 \cdot 10^{+308}} \]

4. Final simplification 0.0%

   \[\leadsto -1.7 \cdot 10^{+308} \]
5. Add Preprocessing

Alternative 4: 24.8% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ 1.7 \cdot 10^{+308} \end{array} \]

FPCore

(FPCore (t) :precision binary64 1.7e+308)

C

double code(double t) {
	return 1.7e+308;
}

Fortran

real(8) function code(t)
    real(8), intent (in) :: t
    code = 1.7d+308
end function

Java

public static double code(double t) {
	return 1.7e+308;
}

Python

def code(t):
	return 1.7e+308

Julia

function code(t)
	return 1.7e+308
end

MATLAB

function tmp = code(t)
	tmp = 1.7e+308;
end

Wolfram

code[t_] := 1.7e+308

Derivation

1. Initial program 36.7%

   \[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. fma-neg 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)} \]

   2. metadata-eval 99.6%

      \[\leadsto \mathsf{fma}\left(1.7 \cdot 10^{+308}, t, \color{blue}{-1.7 \cdot 10^{+308}}\right) \]

   3. add-cube-cbrt 98.1%

      \[\leadsto \color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}} \]

   4. pow2 98.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{2}} \cdot \sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)} \]

4. Applied egg-rr 98.1%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{2} \cdot \sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}} \]
5. Step-by-step derivation

   1. pow-plus 98.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{\left(2 + 1\right)}} \]

   2. metadata-eval 98.1%

      \[\leadsto {\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{\color{blue}{3}} \]

   3. sqr-pow 98.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{\left(\frac{3}{2}\right)}} \]

   4. pow-prod-down 98.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{\left(\frac{3}{2}\right)}} \]

   5. unpow2 98.0%

      \[\leadsto {\color{blue}{\left({\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{2}\right)}}^{\left(\frac{3}{2}\right)} \]

   6. add-cube-cbrt 97.2%

      \[\leadsto {\color{blue}{\left(\left(\sqrt[3]{{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{2}} \cdot \sqrt[3]{{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{2}}\right) \cdot \sqrt[3]{{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{2}}\right)}}^{\left(\frac{3}{2}\right)} \]

   7. pow3 97.2%

      \[\leadsto {\color{blue}{\left({\left(\sqrt[3]{{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{2}}\right)}^{3}\right)}}^{\left(\frac{3}{2}\right)} \]

   8. pow-pow 97.2%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{{\left(\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}\right)}^{2}}\right)}^{\left(3 \cdot \frac{3}{2}\right)}} \]

   9. unpow2 97.2%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}}}\right)}^{\left(3 \cdot \frac{3}{2}\right)} \]

   10. cbrt-prod 96.9%

       \[\leadsto {\color{blue}{\left(\sqrt[3]{\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}} \cdot \sqrt[3]{\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}}\right)}}^{\left(3 \cdot \frac{3}{2}\right)} \]

   11. pow2 96.9%

       \[\leadsto {\color{blue}{\left({\left(\sqrt[3]{\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}}\right)}^{2}\right)}}^{\left(3 \cdot \frac{3}{2}\right)} \]

   12. metadata-eval 96.9%

       \[\leadsto {\left({\left(\sqrt[3]{\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}}\right)}^{2}\right)}^{\left(3 \cdot \color{blue}{1.5}\right)} \]

   13. metadata-eval 96.9%

       \[\leadsto {\left({\left(\sqrt[3]{\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}}\right)}^{2}\right)}^{\color{blue}{4.5}} \]

6. Applied egg-rr 96.9%

   \[\leadsto \color{blue}{{\left({\left(\sqrt[3]{\sqrt[3]{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)}}\right)}^{2}\right)}^{4.5}} \]
7. Step-by-step derivation

   1. fma-def 36.7%

      \[\leadsto {\left({\left(\sqrt[3]{\sqrt[3]{\color{blue}{1.7 \cdot 10^{+308} \cdot t + -1.7 \cdot 10^{+308}}}}\right)}^{2}\right)}^{4.5} \]

   2. *-commutative 36.7%

      \[\leadsto {\left({\left(\sqrt[3]{\sqrt[3]{\color{blue}{t \cdot 1.7 \cdot 10^{+308}} + -1.7 \cdot 10^{+308}}}\right)}^{2}\right)}^{4.5} \]

   3. fma-udef 96.9%

      \[\leadsto {\left({\left(\sqrt[3]{\sqrt[3]{\color{blue}{\mathsf{fma}\left(t, 1.7 \cdot 10^{+308}, -1.7 \cdot 10^{+308}\right)}}}\right)}^{2}\right)}^{4.5} \]

8. Simplified 96.9%

   \[\leadsto \color{blue}{{\left({\left(\sqrt[3]{\sqrt[3]{\mathsf{fma}\left(t, 1.7 \cdot 10^{+308}, -1.7 \cdot 10^{+308}\right)}}\right)}^{2}\right)}^{4.5}} \]

9. Taylor expanded in t around 0 24.8%

   \[\leadsto \color{blue}{1.7 \cdot 10^{+308}} \]

10. Final simplification 24.8%

    \[\leadsto 1.7 \cdot 10^{+308} \]
11. Add Preprocessing

Developer target: 99.6% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right) \end{array} \]

FPCore

(FPCore (t) :precision binary64 (fma 1.7e+308 t (- 1.7e+308)))

C

double code(double t) {
	return fma(1.7e+308, t, -1.7e+308);
}

Julia

function code(t)
	return fma(1.7e+308, t, Float64(-1.7e+308))
end

Wolfram

code[t_] := N[(1.7e+308 * t + (-1.7e+308)), $MachinePrecision]

Reproduce

herbie shell --seed 2024041 
(FPCore (t)
  :name "fma_test2"
  :precision binary64
  :pre (and (<= 1.9 t) (<= t 2.1))

  :herbie-target
  (fma 1.7e+308 t (- 1.7e+308))

  (- (* 1.7e+308 t) 1.7e+308))