fma_test2

Percentage Accurate: 34.7% → 99.6%

Time: 12.6s

Alternatives: 4

Speedup: 1.0×

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: 34.7% 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 33.4%

   \[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308} \]
2. 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. Simplified 99.5%

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

4. Final simplification 99.5%

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

Alternative 2: 36.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.029:\\ \;\;\;\;1.7 \cdot 10^{+308}\\ \mathbf{else}:\\ \;\;\;\;1.7 \cdot 10^{+308} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (t) :precision binary64 (if (<= t 2.029) 1.7e+308 (* 1.7e+308 t)))

C

double code(double t) {
	double tmp;
	if (t <= 2.029) {
		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 <= 2.029d0) 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 <= 2.029) {
		tmp = 1.7e+308;
	} else {
		tmp = 1.7e+308 * t;
	}
	return tmp;
}

Python

def code(t):
	tmp = 0
	if t <= 2.029:
		tmp = 1.7e+308
	else:
		tmp = 1.7e+308 * t
	return tmp

Julia

function code(t)
	tmp = 0.0
	if (t <= 2.029)
		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 <= 2.029)
		tmp = 1.7e+308;
	else
		tmp = 1.7e+308 * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[t_] := If[LessEqual[t, 2.029], 1.7e+308, N[(1.7e+308 * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.0289999999999999

   1. Initial program 22.7%

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

      1. add-cube-cbrt 22.7%

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

      2. pow3 22.7%

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

      3. fma-neg 97.8%

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

      4. metadata-eval 97.8%

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

   3. Applied egg-rr 97.8%

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

      1. add-cube-cbrt 96.2%

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

      2. pow3 96.2%

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

      3. metadata-eval 96.2%

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

      4. metadata-eval 96.2%

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

      5. pow-pow 96.2%

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

      6. metadata-eval 96.2%

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

   5. Applied egg-rr 96.2%

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

      1. fma-def 22.7%

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

      2. *-commutative 22.7%

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

      3. fma-udef 96.2%

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

   7. Simplified 96.2%

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

   8. Taylor expanded in t around 0 25.0%

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

   if 2.0289999999999999 < t

   1. Initial program 75.3%

      \[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308} \]

   2. Taylor expanded in t around inf 75.3%

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

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.029:\\ \;\;\;\;1.7 \cdot 10^{+308}\\ \mathbf{else}:\\ \;\;\;\;1.7 \cdot 10^{+308} \cdot t\\ \end{array} \]

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 33.4%

   \[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308} \]

2. Taylor expanded in t around 0 0.0%

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

3. Final simplification 0.0%

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

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 33.4%

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

   1. add-cube-cbrt 33.4%

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

   2. pow3 33.4%

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

   3. fma-neg 98.0%

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

   4. metadata-eval 98.0%

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

3. Applied egg-rr 98.0%

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

   1. add-cube-cbrt 96.7%

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

   2. pow3 96.7%

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

   3. metadata-eval 96.7%

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

   4. metadata-eval 96.7%

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

   5. pow-pow 96.7%

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

   6. metadata-eval 96.7%

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

5. Applied egg-rr 96.7%

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

   1. fma-def 33.4%

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

   2. *-commutative 33.4%

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

   3. fma-udef 96.7%

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

7. Simplified 96.7%

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

8. Taylor expanded in t around 0 24.8%

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

9. Final simplification 24.8%

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

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 2023305 
(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))