fma_test2

Percentage Accurate: 34.5% → 99.6%

Time: 4.7s

Alternatives: 3

Speedup: 1.5×

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: 34.5% 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, 1.3× 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 34.4%

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

3. Taylor expanded in t around 0

   \[\leadsto \color{blue}{170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot t - 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} \]
4. Step-by-step derivation

   1. metadata-eval N/A

      \[\leadsto 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot t - \color{blue}{170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot 1} \]

   2. metadata-eval N/A

      \[\leadsto 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot t - \color{blue}{\left(\mathsf{neg}\left(-170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right)} \cdot 1 \]

   3. metadata-eval N/A

      \[\leadsto 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot t - \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right)}\right)\right) \cdot 1 \]

   4. lft-mult-inverse N/A

      \[\leadsto 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot t - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right)\right)\right) \cdot \color{blue}{\left(\frac{1}{t} \cdot t\right)} \]

   5. fp-cancel-sign-sub-inv N/A

      \[\leadsto \color{blue}{170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot t + \left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) \cdot \left(\frac{1}{t} \cdot t\right)} \]

   6. associate-*l* N/A

      \[\leadsto 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot t + \color{blue}{\left(\left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) \cdot \frac{1}{t}\right) \cdot t} \]

   7. +-commutative N/A

      \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) \cdot \frac{1}{t}\right) \cdot t + 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot t} \]

   8. distribute-rgt-in N/A

      \[\leadsto \color{blue}{t \cdot \left(\left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) \cdot \frac{1}{t} + 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)} \]

   9. distribute-lft-in N/A

      \[\leadsto \color{blue}{t \cdot \left(\left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) \cdot \frac{1}{t}\right) + t \cdot 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} \]

   10. *-commutative N/A

       \[\leadsto t \cdot \left(\left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) \cdot \frac{1}{t}\right) + \color{blue}{170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot t} \]

   11. fp-cancel-sign-sub-inv N/A

       \[\leadsto \color{blue}{t \cdot \left(\left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) \cdot \frac{1}{t}\right) - \left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) \cdot t} \]

   12. *-commutative N/A

       \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) \cdot \frac{1}{t}\right) \cdot t} - \left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) \cdot t \]

   13. associate-*l* N/A

       \[\leadsto \color{blue}{\left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) \cdot \left(\frac{1}{t} \cdot t\right)} - \left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) \cdot t \]

   14. lft-mult-inverse N/A

       \[\leadsto \left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) \cdot \color{blue}{1} - \left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) \cdot t \]

   15. metadata-eval N/A

       \[\leadsto \color{blue}{-170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} \cdot 1 - \left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) \cdot t \]

   16. metadata-eval N/A

       \[\leadsto \color{blue}{-170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} - \left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) \cdot t \]

   17. metadata-eval N/A

       \[\leadsto \color{blue}{\left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right)} - \left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) \cdot t \]

   18. fp-cancel-sign-sub-inv N/A

       \[\leadsto \color{blue}{\left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right) + 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot t} \]

   19. +-commutative N/A

       \[\leadsto \color{blue}{170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot t + \left(\mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right)} \]

   20. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, t, \mathsf{neg}\left(170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right)\right)} \]

   21. metadata-eval 99.6

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

5. Applied rewrites 99.6%

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

Alternative 2: 34.5% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 34.4%

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

3. Taylor expanded in t around 0

   \[\leadsto \color{blue}{-170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} \]
4. Step-by-step derivation

5. Applied rewrites 0.0%

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

6. Taylor expanded in t around inf

   \[\leadsto \color{blue}{170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot t} \]
7. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{t \cdot 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} \]

   2. lower-*.f64 34.4

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

8. Applied rewrites 34.4%

   \[\leadsto \color{blue}{t \cdot 1.7 \cdot 10^{+308}} \]
9. Add Preprocessing

Alternative 3: 0.0% accurate, 9.0× 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 34.4%

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

3. Taylor expanded in t around 0

   \[\leadsto \color{blue}{-170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} \]
4. Step-by-step derivation

5. Applied rewrites 0.0%

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

Developer Target 1: 99.6% accurate, 1.0× 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 2024343 
(FPCore (t)
  :name "fma_test2"
  :precision binary64
  :pre (and (<= 1.9 t) (<= t 2.1))

  :alt
  (! :herbie-platform default (let ((x 170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)) (fma x t (- x))))

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