FastMath dist3

Percentage Accurate: 97.8% → 100.0%

Time: 5.3s

Alternatives: 6

Speedup: 1.9×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (+ (+ (* d1 d2) (* (+ d3 5.0) d1)) (* d1 32.0)))

C

double code(double d1, double d2, double d3) {
	return ((d1 * d2) + ((d3 + 5.0) * d1)) + (d1 * 32.0);
}

Fortran

real(8) function code(d1, d2, d3)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    code = ((d1 * d2) + ((d3 + 5.0d0) * d1)) + (d1 * 32.0d0)
end function

Java

public static double code(double d1, double d2, double d3) {
	return ((d1 * d2) + ((d3 + 5.0) * d1)) + (d1 * 32.0);
}

Python

def code(d1, d2, d3):
	return ((d1 * d2) + ((d3 + 5.0) * d1)) + (d1 * 32.0)

Julia

function code(d1, d2, d3)
	return Float64(Float64(Float64(d1 * d2) + Float64(Float64(d3 + 5.0) * d1)) + Float64(d1 * 32.0))
end

MATLAB

function tmp = code(d1, d2, d3)
	tmp = ((d1 * d2) + ((d3 + 5.0) * d1)) + (d1 * 32.0);
end

Wolfram

code[d1_, d2_, d3_] := N[(N[(N[(d1 * d2), $MachinePrecision] + N[(N[(d3 + 5.0), $MachinePrecision] * d1), $MachinePrecision]), $MachinePrecision] + N[(d1 * 32.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (+ (+ (* d1 d2) (* (+ d3 5.0) d1)) (* d1 32.0)))

C

double code(double d1, double d2, double d3) {
	return ((d1 * d2) + ((d3 + 5.0) * d1)) + (d1 * 32.0);
}

Fortran

real(8) function code(d1, d2, d3)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    code = ((d1 * d2) + ((d3 + 5.0d0) * d1)) + (d1 * 32.0d0)
end function

Java

public static double code(double d1, double d2, double d3) {
	return ((d1 * d2) + ((d3 + 5.0) * d1)) + (d1 * 32.0);
}

Python

def code(d1, d2, d3):
	return ((d1 * d2) + ((d3 + 5.0) * d1)) + (d1 * 32.0)

Julia

function code(d1, d2, d3)
	return Float64(Float64(Float64(d1 * d2) + Float64(Float64(d3 + 5.0) * d1)) + Float64(d1 * 32.0))
end

MATLAB

function tmp = code(d1, d2, d3)
	tmp = ((d1 * d2) + ((d3 + 5.0) * d1)) + (d1 * 32.0);
end

Wolfram

code[d1_, d2_, d3_] := N[(N[(N[(d1 * d2), $MachinePrecision] + N[(N[(d3 + 5.0), $MachinePrecision] * d1), $MachinePrecision]), $MachinePrecision] + N[(d1 * 32.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ d1 \cdot \left(d3 + \left(d2 + 37\right)\right) \end{array} \]

FPCore

(FPCore (d1 d2 d3) :precision binary64 (* d1 (+ d3 (+ d2 37.0))))

C

double code(double d1, double d2, double d3) {
	return d1 * (d3 + (d2 + 37.0));
}

Fortran

real(8) function code(d1, d2, d3)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    code = d1 * (d3 + (d2 + 37.0d0))
end function

Java

public static double code(double d1, double d2, double d3) {
	return d1 * (d3 + (d2 + 37.0));
}

Python

def code(d1, d2, d3):
	return d1 * (d3 + (d2 + 37.0))

Julia

function code(d1, d2, d3)
	return Float64(d1 * Float64(d3 + Float64(d2 + 37.0)))
end

MATLAB

function tmp = code(d1, d2, d3)
	tmp = d1 * (d3 + (d2 + 37.0));
end

Wolfram

code[d1_, d2_, d3_] := N[(d1 * N[(d3 + N[(d2 + 37.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.0%

   \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
2. Step-by-step derivation

   1. cancel-sign-sub 98.0%

      \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

   2. +-commutative 98.0%

      \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

   3. *-commutative 98.0%

      \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

   4. distribute-lft-out 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

   5. distribute-lft-neg-out 100.0%

      \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

   6. distribute-rgt-neg-in 100.0%

      \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

   7. distribute-lft-out-- 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

   8. associate-+r+ 100.0%

      \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} - \left(-32\right)\right) \]

   9. +-commutative 100.0%

      \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) - \left(-32\right)\right) \]

   10. associate--l+ 100.0%

       \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) - \left(-32\right)\right)\right)} \]

   11. sub-neg 100.0%

       \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(\left(d2 + 5\right) + \left(-\left(-32\right)\right)\right)}\right) \]

   12. metadata-eval 100.0%

       \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \left(-\color{blue}{-32}\right)\right)\right) \]

   13. metadata-eval 100.0%

       \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \color{blue}{32}\right)\right) \]

   14. associate-+l+ 100.0%

       \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

   15. metadata-eval 100.0%

       \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 50.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -2200000:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d2 \leq -2.2 \cdot 10^{-77} \lor \neg \left(d2 \leq -9.8 \cdot 10^{-98}\right) \land \left(d2 \leq -5.2 \cdot 10^{-154} \lor \neg \left(d2 \leq -5.1 \cdot 10^{-256}\right) \land \left(d2 \leq 5 \cdot 10^{-206} \lor \neg \left(d2 \leq 4 \cdot 10^{-39}\right) \land d2 \leq 1.25 \cdot 10^{-33}\right)\right):\\ \;\;\;\;d1 \cdot 37\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d2 -2200000.0)
   (* d1 d2)
   (if (or (<= d2 -2.2e-77)
           (and (not (<= d2 -9.8e-98))
                (or (<= d2 -5.2e-154)
                    (and (not (<= d2 -5.1e-256))
                         (or (<= d2 5e-206)
                             (and (not (<= d2 4e-39)) (<= d2 1.25e-33)))))))
     (* d1 37.0)
     (* d1 d3))))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d2 <= -2200000.0) {
		tmp = d1 * d2;
	} else if ((d2 <= -2.2e-77) || (!(d2 <= -9.8e-98) && ((d2 <= -5.2e-154) || (!(d2 <= -5.1e-256) && ((d2 <= 5e-206) || (!(d2 <= 4e-39) && (d2 <= 1.25e-33))))))) {
		tmp = d1 * 37.0;
	} else {
		tmp = d1 * d3;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8) :: tmp
    if (d2 <= (-2200000.0d0)) then
        tmp = d1 * d2
    else if ((d2 <= (-2.2d-77)) .or. (.not. (d2 <= (-9.8d-98))) .and. (d2 <= (-5.2d-154)) .or. (.not. (d2 <= (-5.1d-256))) .and. (d2 <= 5d-206) .or. (.not. (d2 <= 4d-39)) .and. (d2 <= 1.25d-33)) then
        tmp = d1 * 37.0d0
    else
        tmp = d1 * d3
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3) {
	double tmp;
	if (d2 <= -2200000.0) {
		tmp = d1 * d2;
	} else if ((d2 <= -2.2e-77) || (!(d2 <= -9.8e-98) && ((d2 <= -5.2e-154) || (!(d2 <= -5.1e-256) && ((d2 <= 5e-206) || (!(d2 <= 4e-39) && (d2 <= 1.25e-33))))))) {
		tmp = d1 * 37.0;
	} else {
		tmp = d1 * d3;
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d2 <= -2200000.0:
		tmp = d1 * d2
	elif (d2 <= -2.2e-77) or (not (d2 <= -9.8e-98) and ((d2 <= -5.2e-154) or (not (d2 <= -5.1e-256) and ((d2 <= 5e-206) or (not (d2 <= 4e-39) and (d2 <= 1.25e-33)))))):
		tmp = d1 * 37.0
	else:
		tmp = d1 * d3
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d2 <= -2200000.0)
		tmp = Float64(d1 * d2);
	elseif ((d2 <= -2.2e-77) || (!(d2 <= -9.8e-98) && ((d2 <= -5.2e-154) || (!(d2 <= -5.1e-256) && ((d2 <= 5e-206) || (!(d2 <= 4e-39) && (d2 <= 1.25e-33)))))))
		tmp = Float64(d1 * 37.0);
	else
		tmp = Float64(d1 * d3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3)
	tmp = 0.0;
	if (d2 <= -2200000.0)
		tmp = d1 * d2;
	elseif ((d2 <= -2.2e-77) || (~((d2 <= -9.8e-98)) && ((d2 <= -5.2e-154) || (~((d2 <= -5.1e-256)) && ((d2 <= 5e-206) || (~((d2 <= 4e-39)) && (d2 <= 1.25e-33)))))))
		tmp = d1 * 37.0;
	else
		tmp = d1 * d3;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d2, -2200000.0], N[(d1 * d2), $MachinePrecision], If[Or[LessEqual[d2, -2.2e-77], And[N[Not[LessEqual[d2, -9.8e-98]], $MachinePrecision], Or[LessEqual[d2, -5.2e-154], And[N[Not[LessEqual[d2, -5.1e-256]], $MachinePrecision], Or[LessEqual[d2, 5e-206], And[N[Not[LessEqual[d2, 4e-39]], $MachinePrecision], LessEqual[d2, 1.25e-33]]]]]]], N[(d1 * 37.0), $MachinePrecision], N[(d1 * d3), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d2 < -2.2e6

   1. Initial program 95.7%

      \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
   2. Step-by-step derivation

      1. cancel-sign-sub 95.7%

         \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

      2. +-commutative 95.7%

         \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

      3. *-commutative 95.7%

         \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

      4. distribute-lft-out 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

      5. distribute-lft-neg-out 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

      7. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

      8. associate-+r+ 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} - \left(-32\right)\right) \]

      9. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) - \left(-32\right)\right) \]

      10. associate--l+ 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) - \left(-32\right)\right)\right)} \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(\left(d2 + 5\right) + \left(-\left(-32\right)\right)\right)}\right) \]

      12. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \left(-\color{blue}{-32}\right)\right)\right) \]

      13. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \color{blue}{32}\right)\right) \]

      14. associate-+l+ 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

      15. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d2 around inf 77.2%

      \[\leadsto \color{blue}{d1 \cdot d2} \]

   if -2.2e6 < d2 < -2.20000000000000007e-77 or -9.80000000000000028e-98 < d2 < -5.2e-154 or -5.10000000000000011e-256 < d2 < 5e-206 or 3.99999999999999972e-39 < d2 < 1.25000000000000007e-33

   1. Initial program 99.9%

      \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
   2. Step-by-step derivation

      1. cancel-sign-sub 99.9%

         \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

      2. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

      3. *-commutative 99.9%

         \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

      4. distribute-lft-out 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

      5. distribute-lft-neg-out 99.9%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

      6. distribute-rgt-neg-in 99.9%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

      7. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

      8. associate-+r+ 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} - \left(-32\right)\right) \]

      9. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) - \left(-32\right)\right) \]

      10. associate--l+ 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) - \left(-32\right)\right)\right)} \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(\left(d2 + 5\right) + \left(-\left(-32\right)\right)\right)}\right) \]

      12. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \left(-\color{blue}{-32}\right)\right)\right) \]

      13. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \color{blue}{32}\right)\right) \]

      14. associate-+l+ 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

      15. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d3 around 0 55.4%

      \[\leadsto \color{blue}{d1 \cdot \left(37 + d2\right)} \]

   6. Taylor expanded in d2 around 0 52.8%

      \[\leadsto \color{blue}{37 \cdot d1} \]
   7. Step-by-step derivation

      1. *-commutative 52.8%

         \[\leadsto \color{blue}{d1 \cdot 37} \]

   8. Simplified 52.8%

      \[\leadsto \color{blue}{d1 \cdot 37} \]

   if -2.20000000000000007e-77 < d2 < -9.80000000000000028e-98 or -5.2e-154 < d2 < -5.10000000000000011e-256 or 5e-206 < d2 < 3.99999999999999972e-39 or 1.25000000000000007e-33 < d2

   1. Initial program 98.3%

      \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
   2. Step-by-step derivation

      1. cancel-sign-sub 98.3%

         \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

      2. +-commutative 98.3%

         \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

      3. *-commutative 98.3%

         \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

      4. distribute-lft-out 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

      5. distribute-lft-neg-out 99.9%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

      6. distribute-rgt-neg-in 99.9%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

      7. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

      8. associate-+r+ 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} - \left(-32\right)\right) \]

      9. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) - \left(-32\right)\right) \]

      10. associate--l+ 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) - \left(-32\right)\right)\right)} \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(\left(d2 + 5\right) + \left(-\left(-32\right)\right)\right)}\right) \]

      12. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \left(-\color{blue}{-32}\right)\right)\right) \]

      13. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \color{blue}{32}\right)\right) \]

      14. associate-+l+ 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

      15. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d3 around inf 46.8%

      \[\leadsto \color{blue}{d1 \cdot d3} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -2200000:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d2 \leq -2.2 \cdot 10^{-77} \lor \neg \left(d2 \leq -9.8 \cdot 10^{-98}\right) \land \left(d2 \leq -5.2 \cdot 10^{-154} \lor \neg \left(d2 \leq -5.1 \cdot 10^{-256}\right) \land \left(d2 \leq 5 \cdot 10^{-206} \lor \neg \left(d2 \leq 4 \cdot 10^{-39}\right) \land d2 \leq 1.25 \cdot 10^{-33}\right)\right):\\ \;\;\;\;d1 \cdot 37\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d3 \leq 58000 \lor \neg \left(d3 \leq 6.5 \cdot 10^{+42}\right) \land d3 \leq 5 \cdot 10^{+52}:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (or (<= d3 58000.0) (and (not (<= d3 6.5e+42)) (<= d3 5e+52)))
   (* d1 (+ d2 37.0))
   (* d1 d3)))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if ((d3 <= 58000.0) || (!(d3 <= 6.5e+42) && (d3 <= 5e+52))) {
		tmp = d1 * (d2 + 37.0);
	} else {
		tmp = d1 * d3;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8) :: tmp
    if ((d3 <= 58000.0d0) .or. (.not. (d3 <= 6.5d+42)) .and. (d3 <= 5d+52)) then
        tmp = d1 * (d2 + 37.0d0)
    else
        tmp = d1 * d3
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3) {
	double tmp;
	if ((d3 <= 58000.0) || (!(d3 <= 6.5e+42) && (d3 <= 5e+52))) {
		tmp = d1 * (d2 + 37.0);
	} else {
		tmp = d1 * d3;
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if (d3 <= 58000.0) or (not (d3 <= 6.5e+42) and (d3 <= 5e+52)):
		tmp = d1 * (d2 + 37.0)
	else:
		tmp = d1 * d3
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if ((d3 <= 58000.0) || (!(d3 <= 6.5e+42) && (d3 <= 5e+52)))
		tmp = Float64(d1 * Float64(d2 + 37.0));
	else
		tmp = Float64(d1 * d3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3)
	tmp = 0.0;
	if ((d3 <= 58000.0) || (~((d3 <= 6.5e+42)) && (d3 <= 5e+52)))
		tmp = d1 * (d2 + 37.0);
	else
		tmp = d1 * d3;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[Or[LessEqual[d3, 58000.0], And[N[Not[LessEqual[d3, 6.5e+42]], $MachinePrecision], LessEqual[d3, 5e+52]]], N[(d1 * N[(d2 + 37.0), $MachinePrecision]), $MachinePrecision], N[(d1 * d3), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d3 < 58000 or 6.50000000000000052e42 < d3 < 5e52

   1. Initial program 98.9%

      \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
   2. Step-by-step derivation

      1. cancel-sign-sub 98.9%

         \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

      2. +-commutative 98.9%

         \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

      3. *-commutative 98.9%

         \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

      4. distribute-lft-out 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

      5. distribute-lft-neg-out 99.9%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

      6. distribute-rgt-neg-in 99.9%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

      7. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

      8. associate-+r+ 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} - \left(-32\right)\right) \]

      9. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) - \left(-32\right)\right) \]

      10. associate--l+ 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) - \left(-32\right)\right)\right)} \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(\left(d2 + 5\right) + \left(-\left(-32\right)\right)\right)}\right) \]

      12. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \left(-\color{blue}{-32}\right)\right)\right) \]

      13. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \color{blue}{32}\right)\right) \]

      14. associate-+l+ 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

      15. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d3 around 0 72.7%

      \[\leadsto \color{blue}{d1 \cdot \left(37 + d2\right)} \]

   if 58000 < d3 < 6.50000000000000052e42 or 5e52 < d3

   1. Initial program 94.2%

      \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
   2. Step-by-step derivation

      1. cancel-sign-sub 94.2%

         \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

      2. +-commutative 94.2%

         \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

      3. *-commutative 94.2%

         \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

      4. distribute-lft-out 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

      5. distribute-lft-neg-out 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

      7. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

      8. associate-+r+ 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} - \left(-32\right)\right) \]

      9. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) - \left(-32\right)\right) \]

      10. associate--l+ 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) - \left(-32\right)\right)\right)} \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(\left(d2 + 5\right) + \left(-\left(-32\right)\right)\right)}\right) \]

      12. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \left(-\color{blue}{-32}\right)\right)\right) \]

      13. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \color{blue}{32}\right)\right) \]

      14. associate-+l+ 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

      15. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d3 around inf 84.3%

      \[\leadsto \color{blue}{d1 \cdot d3} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq 58000 \lor \neg \left(d3 \leq 6.5 \cdot 10^{+42}\right) \land d3 \leq 5 \cdot 10^{+52}:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -8000000:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d3 + 37\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d2 -8000000.0) (* d1 (+ d2 37.0)) (* d1 (+ d3 37.0))))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d2 <= -8000000.0) {
		tmp = d1 * (d2 + 37.0);
	} else {
		tmp = d1 * (d3 + 37.0);
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8) :: tmp
    if (d2 <= (-8000000.0d0)) then
        tmp = d1 * (d2 + 37.0d0)
    else
        tmp = d1 * (d3 + 37.0d0)
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3) {
	double tmp;
	if (d2 <= -8000000.0) {
		tmp = d1 * (d2 + 37.0);
	} else {
		tmp = d1 * (d3 + 37.0);
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d2 <= -8000000.0:
		tmp = d1 * (d2 + 37.0)
	else:
		tmp = d1 * (d3 + 37.0)
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d2 <= -8000000.0)
		tmp = Float64(d1 * Float64(d2 + 37.0));
	else
		tmp = Float64(d1 * Float64(d3 + 37.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3)
	tmp = 0.0;
	if (d2 <= -8000000.0)
		tmp = d1 * (d2 + 37.0);
	else
		tmp = d1 * (d3 + 37.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d2, -8000000.0], N[(d1 * N[(d2 + 37.0), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d3 + 37.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -8e6

   1. Initial program 95.7%

      \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
   2. Step-by-step derivation

      1. cancel-sign-sub 95.7%

         \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

      2. +-commutative 95.7%

         \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

      3. *-commutative 95.7%

         \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

      4. distribute-lft-out 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

      5. distribute-lft-neg-out 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

      7. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

      8. associate-+r+ 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} - \left(-32\right)\right) \]

      9. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) - \left(-32\right)\right) \]

      10. associate--l+ 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) - \left(-32\right)\right)\right)} \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(\left(d2 + 5\right) + \left(-\left(-32\right)\right)\right)}\right) \]

      12. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \left(-\color{blue}{-32}\right)\right)\right) \]

      13. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \color{blue}{32}\right)\right) \]

      14. associate-+l+ 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

      15. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d3 around 0 79.1%

      \[\leadsto \color{blue}{d1 \cdot \left(37 + d2\right)} \]

   if -8e6 < d2

   1. Initial program 98.8%

      \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
   2. Step-by-step derivation

      1. cancel-sign-sub 98.8%

         \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

      2. +-commutative 98.8%

         \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

      3. *-commutative 98.8%

         \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

      4. distribute-lft-out 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

      5. distribute-lft-neg-out 99.9%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

      6. distribute-rgt-neg-in 99.9%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

      7. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

      8. associate-+r+ 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} - \left(-32\right)\right) \]

      9. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) - \left(-32\right)\right) \]

      10. associate--l+ 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) - \left(-32\right)\right)\right)} \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(\left(d2 + 5\right) + \left(-\left(-32\right)\right)\right)}\right) \]

      12. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \left(-\color{blue}{-32}\right)\right)\right) \]

      13. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \color{blue}{32}\right)\right) \]

      14. associate-+l+ 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

      15. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d2 around 0 77.6%

      \[\leadsto \color{blue}{d1 \cdot \left(37 + d3\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -8000000:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d3 + 37\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 44.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -132000000000:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot 37\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d2 -132000000000.0) (* d1 d2) (* d1 37.0)))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d2 <= -132000000000.0) {
		tmp = d1 * d2;
	} else {
		tmp = d1 * 37.0;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8) :: tmp
    if (d2 <= (-132000000000.0d0)) then
        tmp = d1 * d2
    else
        tmp = d1 * 37.0d0
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3) {
	double tmp;
	if (d2 <= -132000000000.0) {
		tmp = d1 * d2;
	} else {
		tmp = d1 * 37.0;
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d2 <= -132000000000.0:
		tmp = d1 * d2
	else:
		tmp = d1 * 37.0
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d2 <= -132000000000.0)
		tmp = Float64(d1 * d2);
	else
		tmp = Float64(d1 * 37.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3)
	tmp = 0.0;
	if (d2 <= -132000000000.0)
		tmp = d1 * d2;
	else
		tmp = d1 * 37.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d2, -132000000000.0], N[(d1 * d2), $MachinePrecision], N[(d1 * 37.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -1.32e11

   1. Initial program 95.5%

      \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
   2. Step-by-step derivation

      1. cancel-sign-sub 95.5%

         \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

      2. +-commutative 95.5%

         \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

      3. *-commutative 95.5%

         \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

      4. distribute-lft-out 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

      5. distribute-lft-neg-out 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

      7. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

      8. associate-+r+ 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} - \left(-32\right)\right) \]

      9. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) - \left(-32\right)\right) \]

      10. associate--l+ 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) - \left(-32\right)\right)\right)} \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(\left(d2 + 5\right) + \left(-\left(-32\right)\right)\right)}\right) \]

      12. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \left(-\color{blue}{-32}\right)\right)\right) \]

      13. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \color{blue}{32}\right)\right) \]

      14. associate-+l+ 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

      15. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d2 around inf 78.1%

      \[\leadsto \color{blue}{d1 \cdot d2} \]

   if -1.32e11 < d2

   1. Initial program 98.9%

      \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
   2. Step-by-step derivation

      1. cancel-sign-sub 98.9%

         \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

      2. +-commutative 98.9%

         \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

      3. *-commutative 98.9%

         \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

      4. distribute-lft-out 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

      5. distribute-lft-neg-out 99.9%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

      6. distribute-rgt-neg-in 99.9%

         \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

      7. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

      8. associate-+r+ 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} - \left(-32\right)\right) \]

      9. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) - \left(-32\right)\right) \]

      10. associate--l+ 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) - \left(-32\right)\right)\right)} \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(\left(d2 + 5\right) + \left(-\left(-32\right)\right)\right)}\right) \]

      12. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \left(-\color{blue}{-32}\right)\right)\right) \]

      13. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \color{blue}{32}\right)\right) \]

      14. associate-+l+ 100.0%

          \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

      15. metadata-eval 100.0%

          \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in d3 around 0 56.6%

      \[\leadsto \color{blue}{d1 \cdot \left(37 + d2\right)} \]

   6. Taylor expanded in d2 around 0 32.8%

      \[\leadsto \color{blue}{37 \cdot d1} \]
   7. Step-by-step derivation

      1. *-commutative 32.8%

         \[\leadsto \color{blue}{d1 \cdot 37} \]

   8. Simplified 32.8%

      \[\leadsto \color{blue}{d1 \cdot 37} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 26.3% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ d1 \cdot 37 \end{array} \]

FPCore

(FPCore (d1 d2 d3) :precision binary64 (* d1 37.0))

C

double code(double d1, double d2, double d3) {
	return d1 * 37.0;
}

Fortran

real(8) function code(d1, d2, d3)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    code = d1 * 37.0d0
end function

Java

public static double code(double d1, double d2, double d3) {
	return d1 * 37.0;
}

Python

def code(d1, d2, d3):
	return d1 * 37.0

Julia

function code(d1, d2, d3)
	return Float64(d1 * 37.0)
end

MATLAB

function tmp = code(d1, d2, d3)
	tmp = d1 * 37.0;
end

Wolfram

code[d1_, d2_, d3_] := N[(d1 * 37.0), $MachinePrecision]

Derivation

1. Initial program 98.0%

   \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32 \]
2. Step-by-step derivation

   1. cancel-sign-sub 98.0%

      \[\leadsto \color{blue}{\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) - \left(-d1\right) \cdot 32} \]

   2. +-commutative 98.0%

      \[\leadsto \color{blue}{\left(\left(d3 + 5\right) \cdot d1 + d1 \cdot d2\right)} - \left(-d1\right) \cdot 32 \]

   3. *-commutative 98.0%

      \[\leadsto \left(\color{blue}{d1 \cdot \left(d3 + 5\right)} + d1 \cdot d2\right) - \left(-d1\right) \cdot 32 \]

   4. distribute-lft-out 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 5\right) + d2\right)} - \left(-d1\right) \cdot 32 \]

   5. distribute-lft-neg-out 100.0%

      \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{\left(-d1 \cdot 32\right)} \]

   6. distribute-rgt-neg-in 100.0%

      \[\leadsto d1 \cdot \left(\left(d3 + 5\right) + d2\right) - \color{blue}{d1 \cdot \left(-32\right)} \]

   7. distribute-lft-out-- 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(\left(d3 + 5\right) + d2\right) - \left(-32\right)\right)} \]

   8. associate-+r+ 100.0%

      \[\leadsto d1 \cdot \left(\color{blue}{\left(d3 + \left(5 + d2\right)\right)} - \left(-32\right)\right) \]

   9. +-commutative 100.0%

      \[\leadsto d1 \cdot \left(\left(d3 + \color{blue}{\left(d2 + 5\right)}\right) - \left(-32\right)\right) \]

   10. associate--l+ 100.0%

       \[\leadsto d1 \cdot \color{blue}{\left(d3 + \left(\left(d2 + 5\right) - \left(-32\right)\right)\right)} \]

   11. sub-neg 100.0%

       \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(\left(d2 + 5\right) + \left(-\left(-32\right)\right)\right)}\right) \]

   12. metadata-eval 100.0%

       \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \left(-\color{blue}{-32}\right)\right)\right) \]

   13. metadata-eval 100.0%

       \[\leadsto d1 \cdot \left(d3 + \left(\left(d2 + 5\right) + \color{blue}{32}\right)\right) \]

   14. associate-+l+ 100.0%

       \[\leadsto d1 \cdot \left(d3 + \color{blue}{\left(d2 + \left(5 + 32\right)\right)}\right) \]

   15. metadata-eval 100.0%

       \[\leadsto d1 \cdot \left(d3 + \left(d2 + \color{blue}{37}\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{d1 \cdot \left(d3 + \left(d2 + 37\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in d3 around 0 62.2%

   \[\leadsto \color{blue}{d1 \cdot \left(37 + d2\right)} \]

6. Taylor expanded in d2 around 0 24.6%

   \[\leadsto \color{blue}{37 \cdot d1} \]
7. Step-by-step derivation

   1. *-commutative 24.6%

      \[\leadsto \color{blue}{d1 \cdot 37} \]

8. Simplified 24.6%

   \[\leadsto \color{blue}{d1 \cdot 37} \]
9. Add Preprocessing

Developer target: 100.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ d1 \cdot \left(\left(37 + d3\right) + d2\right) \end{array} \]

FPCore

(FPCore (d1 d2 d3) :precision binary64 (* d1 (+ (+ 37.0 d3) d2)))

C

double code(double d1, double d2, double d3) {
	return d1 * ((37.0 + d3) + d2);
}

Fortran

real(8) function code(d1, d2, d3)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    code = d1 * ((37.0d0 + d3) + d2)
end function

Java

public static double code(double d1, double d2, double d3) {
	return d1 * ((37.0 + d3) + d2);
}

Python

def code(d1, d2, d3):
	return d1 * ((37.0 + d3) + d2)

Julia

function code(d1, d2, d3)
	return Float64(d1 * Float64(Float64(37.0 + d3) + d2))
end

MATLAB

function tmp = code(d1, d2, d3)
	tmp = d1 * ((37.0 + d3) + d2);
end

Wolfram

code[d1_, d2_, d3_] := N[(d1 * N[(N[(37.0 + d3), $MachinePrecision] + d2), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024103 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  :precision binary64

  :alt
  (* d1 (+ (+ 37.0 d3) d2))

  (+ (+ (* d1 d2) (* (+ d3 5.0) d1)) (* d1 32.0)))