FastMath dist3

Percentage Accurate: 97.9% → 100.0%

Time: 7.5s

Alternatives: 6

Speedup: 1.9×

• 20.9% 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: 97.9% 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 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. Add Preprocessing

Alternative 2: 51.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -38:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d2 \leq -1.25 \cdot 10^{-26} \lor \neg \left(d2 \leq -1.05 \cdot 10^{-36}\right) \land \left(d2 \leq -7.8 \cdot 10^{-41} \lor \neg \left(d2 \leq -3.4 \cdot 10^{-45}\right) \land \left(d2 \leq -1.5 \cdot 10^{-61} \lor \neg \left(d2 \leq -1 \cdot 10^{-64}\right) \land \left(d2 \leq -1.7 \cdot 10^{-81} \lor \neg \left(d2 \leq -1.7 \cdot 10^{-82}\right) \land \left(d2 \leq -3.9 \cdot 10^{-121} \lor \neg \left(d2 \leq -6.5 \cdot 10^{-136}\right) \land \left(d2 \leq -5.9 \cdot 10^{-140} \lor \neg \left(d2 \leq -1.05 \cdot 10^{-146}\right) \land \left(d2 \leq -2.55 \cdot 10^{-173} \lor \neg \left(d2 \leq -3.3 \cdot 10^{-190}\right) \land \left(d2 \leq -3.15 \cdot 10^{-198} \lor \neg \left(d2 \leq -1.2 \cdot 10^{-211}\right) \land \left(d2 \leq -3 \cdot 10^{-216} \lor \neg \left(d2 \leq -7.6 \cdot 10^{-226}\right) \land \left(d2 \leq -3.35 \cdot 10^{-239} \lor \neg \left(d2 \leq -1.75 \cdot 10^{-239}\right) \land \left(d2 \leq -1.2 \cdot 10^{-248} \lor \neg \left(d2 \leq -9.2 \cdot 10^{-253}\right) \land \left(d2 \leq -7.2 \cdot 10^{-258} \lor \neg \left(d2 \leq -1.3 \cdot 10^{-280}\right) \land \left(d2 \leq -9.8 \cdot 10^{-291} \lor \neg \left(d2 \leq -5.2 \cdot 10^{-301}\right) \land \left(d2 \leq -1.5 \cdot 10^{-306} \lor \neg \left(d2 \leq 2.4 \cdot 10^{-295}\right) \land \left(d2 \leq 3.7 \cdot 10^{-291} \lor \neg \left(d2 \leq 1.5 \cdot 10^{-286}\right) \land \left(d2 \leq 2.6 \cdot 10^{-286} \lor \neg \left(d2 \leq 1.05 \cdot 10^{-285}\right) \land \left(d2 \leq 1.35 \cdot 10^{-284} \lor \neg \left(d2 \leq 1.8 \cdot 10^{-283}\right) \land \left(d2 \leq 5.8 \cdot 10^{-280} \lor \neg \left(d2 \leq 8.5 \cdot 10^{-232}\right) \land \left(d2 \leq 3.7 \cdot 10^{-215} \lor \neg \left(d2 \leq 2 \cdot 10^{-210}\right) \land \left(d2 \leq 4.5 \cdot 10^{-207} \lor \neg \left(d2 \leq 2.3 \cdot 10^{-191}\right) \land \left(d2 \leq 1.5 \cdot 10^{-169} \lor \neg \left(d2 \leq 3.4 \cdot 10^{-167}\right) \land \left(d2 \leq 2.55 \cdot 10^{-160} \lor \neg \left(d2 \leq 4.6 \cdot 10^{-159}\right) \land \left(d2 \leq 1.05 \cdot 10^{-134} \lor \neg \left(d2 \leq 3.2 \cdot 10^{-73}\right) \land d2 \leq 1.32 \cdot 10^{-64}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right):\\ \;\;\;\;d1 \cdot 37\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d2 -38.0)
   (* d1 d2)
   (if (or (<= d2 -1.25e-26)
           (and (not (<= d2 -1.05e-36))
                (or (<= d2 -7.8e-41)
                    (and (not (<= d2 -3.4e-45))
                         (or (<= d2 -1.5e-61)
                             (and (not (<= d2 -1e-64))
                                  (or (<= d2 -1.7e-81)
                                      (and (not (<= d2 -1.7e-82))
                                           (or (<= d2 -3.9e-121)
                                               (and (not (<= d2 -6.5e-136))
                                                    (or (<= d2 -5.9e-140)
                                                        (and (not
                                                              (<=
                                                               d2
                                                               -1.05e-146))
                                                             (or (<=
                                                                  d2
                                                                  -2.55e-173)
                                                                 (and (not
                                                                       (<=
                                                                        d2
                                                                        -3.3e-190))
                                                                      (or (<=
                                                                           d2
                                                                           -3.15e-198)
                                                                          (and (not
                                                                                (<=
                                                                                 d2
                                                                                 -1.2e-211))
                                                                               (or (<=
                                                                                    d2
                                                                                    -3e-216)
                                                                                   (and (not
                                                                                         (<=
                                                                                          d2
                                                                                          -7.6e-226))
                                                                                        (or (<=
                                                                                             d2
                                                                                             -3.35e-239)
                                                                                            (and (not
                                                                                                  (<=
                                                                                                   d2
                                                                                                   -1.75e-239))
                                                                                                 (or (<=
                                                                                                      d2
                                                                                                      -1.2e-248)
                                                                                                     (and (not
                                                                                                           (<=
                                                                                                            d2
                                                                                                            -9.2e-253))
                                                                                                          (or (<=
                                                                                                               d2
                                                                                                               -7.2e-258)
                                                                                                              (and (not
                                                                                                                    (<=
                                                                                                                     d2
                                                                                                                     -1.3e-280))
                                                                                                                   (or (<=
                                                                                                                        d2
                                                                                                                        -9.8e-291)
                                                                                                                       (and (not
                                                                                                                             (<=
                                                                                                                              d2
                                                                                                                              -5.2e-301))
                                                                                                                            (or (<=
                                                                                                                                 d2
                                                                                                                                 -1.5e-306)
                                                                                                                                (and (not
                                                                                                                                      (<=
                                                                                                                                       d2
                                                                                                                                       2.4e-295))
                                                                                                                                     (or (<=
                                                                                                                                          d2
                                                                                                                                          3.7e-291)
                                                                                                                                         (and (not
                                                                                                                                               (<=
                                                                                                                                                d2
                                                                                                                                                1.5e-286))
                                                                                                                                              (or (<=
                                                                                                                                                   d2
                                                                                                                                                   2.6e-286)
                                                                                                                                                  (and (not
                                                                                                                                                        (<=
                                                                                                                                                         d2
                                                                                                                                                         1.05e-285))
                                                                                                                                                       (or (<=
                                                                                                                                                            d2
                                                                                                                                                            1.35e-284)
                                                                                                                                                           (and (not
                                                                                                                                                                 (<=
                                                                                                                                                                  d2
                                                                                                                                                                  1.8e-283))
                                                                                                                                                                (or (<=
                                                                                                                                                                     d2
                                                                                                                                                                     5.8e-280)
                                                                                                                                                                    (and (not
                                                                                                                                                                          (<=
                                                                                                                                                                           d2
                                                                                                                                                                           8.5e-232))
                                                                                                                                                                         (or (<=
                                                                                                                                                                              d2
                                                                                                                                                                              3.7e-215)
                                                                                                                                                                             (and (not
                                                                                                                                                                                   (<=
                                                                                                                                                                                    d2
                                                                                                                                                                                    2e-210))
                                                                                                                                                                                  (or (<=
                                                                                                                                                                                       d2
                                                                                                                                                                                       4.5e-207)
                                                                                                                                                                                      (and (not
                                                                                                                                                                                            (<=
                                                                                                                                                                                             d2
                                                                                                                                                                                             2.3e-191))
                                                                                                                                                                                           (or (<=
                                                                                                                                                                                                d2
                                                                                                                                                                                                1.5e-169)
                                                                                                                                                                                               (and (not
                                                                                                                                                                                                     (<=
                                                                                                                                                                                                      d2
                                                                                                                                                                                                      3.4e-167))
                                                                                                                                                                                                    (or (<=
                                                                                                                                                                                                         d2
                                                                                                                                                                                                         2.55e-160)
                                                                                                                                                                                                        (and (not
                                                                                                                                                                                                              (<=
                                                                                                                                                                                                               d2
                                                                                                                                                                                                               4.6e-159))
                                                                                                                                                                                                             (or (<=
                                                                                                                                                                                                                  d2
                                                                                                                                                                                                                  1.05e-134)
                                                                                                                                                                                                                 (and (not
                                                                                                                                                                                                                       (<=
                                                                                                                                                                                                                        d2
                                                                                                                                                                                                                        3.2e-73))
                                                                                                                                                                                                                      (<=
                                                                                                                                                                                                                       d2
                                                                                                                                                                                                                       1.32e-64)))))))))))))))))))))))))))))))))))))))))))))))
     (* d1 37.0)
     (* d1 d3))))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d2 <= -38.0) {
		tmp = d1 * d2;
	} else if ((d2 <= -1.25e-26) || (!(d2 <= -1.05e-36) && ((d2 <= -7.8e-41) || (!(d2 <= -3.4e-45) && ((d2 <= -1.5e-61) || (!(d2 <= -1e-64) && ((d2 <= -1.7e-81) || (!(d2 <= -1.7e-82) && ((d2 <= -3.9e-121) || (!(d2 <= -6.5e-136) && ((d2 <= -5.9e-140) || (!(d2 <= -1.05e-146) && ((d2 <= -2.55e-173) || (!(d2 <= -3.3e-190) && ((d2 <= -3.15e-198) || (!(d2 <= -1.2e-211) && ((d2 <= -3e-216) || (!(d2 <= -7.6e-226) && ((d2 <= -3.35e-239) || (!(d2 <= -1.75e-239) && ((d2 <= -1.2e-248) || (!(d2 <= -9.2e-253) && ((d2 <= -7.2e-258) || (!(d2 <= -1.3e-280) && ((d2 <= -9.8e-291) || (!(d2 <= -5.2e-301) && ((d2 <= -1.5e-306) || (!(d2 <= 2.4e-295) && ((d2 <= 3.7e-291) || (!(d2 <= 1.5e-286) && ((d2 <= 2.6e-286) || (!(d2 <= 1.05e-285) && ((d2 <= 1.35e-284) || (!(d2 <= 1.8e-283) && ((d2 <= 5.8e-280) || (!(d2 <= 8.5e-232) && ((d2 <= 3.7e-215) || (!(d2 <= 2e-210) && ((d2 <= 4.5e-207) || (!(d2 <= 2.3e-191) && ((d2 <= 1.5e-169) || (!(d2 <= 3.4e-167) && ((d2 <= 2.55e-160) || (!(d2 <= 4.6e-159) && ((d2 <= 1.05e-134) || (!(d2 <= 3.2e-73) && (d2 <= 1.32e-64))))))))))))))))))))))))))))))))))))))))))))))) {
		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 <= (-38.0d0)) then
        tmp = d1 * d2
    else if ((d2 <= (-1.25d-26)) .or. (.not. (d2 <= (-1.05d-36))) .and. (d2 <= (-7.8d-41)) .or. (.not. (d2 <= (-3.4d-45))) .and. (d2 <= (-1.5d-61)) .or. (.not. (d2 <= (-1d-64))) .and. (d2 <= (-1.7d-81)) .or. (.not. (d2 <= (-1.7d-82))) .and. (d2 <= (-3.9d-121)) .or. (.not. (d2 <= (-6.5d-136))) .and. (d2 <= (-5.9d-140)) .or. (.not. (d2 <= (-1.05d-146))) .and. (d2 <= (-2.55d-173)) .or. (.not. (d2 <= (-3.3d-190))) .and. (d2 <= (-3.15d-198)) .or. (.not. (d2 <= (-1.2d-211))) .and. (d2 <= (-3d-216)) .or. (.not. (d2 <= (-7.6d-226))) .and. (d2 <= (-3.35d-239)) .or. (.not. (d2 <= (-1.75d-239))) .and. (d2 <= (-1.2d-248)) .or. (.not. (d2 <= (-9.2d-253))) .and. (d2 <= (-7.2d-258)) .or. (.not. (d2 <= (-1.3d-280))) .and. (d2 <= (-9.8d-291)) .or. (.not. (d2 <= (-5.2d-301))) .and. (d2 <= (-1.5d-306)) .or. (.not. (d2 <= 2.4d-295)) .and. (d2 <= 3.7d-291) .or. (.not. (d2 <= 1.5d-286)) .and. (d2 <= 2.6d-286) .or. (.not. (d2 <= 1.05d-285)) .and. (d2 <= 1.35d-284) .or. (.not. (d2 <= 1.8d-283)) .and. (d2 <= 5.8d-280) .or. (.not. (d2 <= 8.5d-232)) .and. (d2 <= 3.7d-215) .or. (.not. (d2 <= 2d-210)) .and. (d2 <= 4.5d-207) .or. (.not. (d2 <= 2.3d-191)) .and. (d2 <= 1.5d-169) .or. (.not. (d2 <= 3.4d-167)) .and. (d2 <= 2.55d-160) .or. (.not. (d2 <= 4.6d-159)) .and. (d2 <= 1.05d-134) .or. (.not. (d2 <= 3.2d-73)) .and. (d2 <= 1.32d-64)) 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 <= -38.0) {
		tmp = d1 * d2;
	} else if ((d2 <= -1.25e-26) || (!(d2 <= -1.05e-36) && ((d2 <= -7.8e-41) || (!(d2 <= -3.4e-45) && ((d2 <= -1.5e-61) || (!(d2 <= -1e-64) && ((d2 <= -1.7e-81) || (!(d2 <= -1.7e-82) && ((d2 <= -3.9e-121) || (!(d2 <= -6.5e-136) && ((d2 <= -5.9e-140) || (!(d2 <= -1.05e-146) && ((d2 <= -2.55e-173) || (!(d2 <= -3.3e-190) && ((d2 <= -3.15e-198) || (!(d2 <= -1.2e-211) && ((d2 <= -3e-216) || (!(d2 <= -7.6e-226) && ((d2 <= -3.35e-239) || (!(d2 <= -1.75e-239) && ((d2 <= -1.2e-248) || (!(d2 <= -9.2e-253) && ((d2 <= -7.2e-258) || (!(d2 <= -1.3e-280) && ((d2 <= -9.8e-291) || (!(d2 <= -5.2e-301) && ((d2 <= -1.5e-306) || (!(d2 <= 2.4e-295) && ((d2 <= 3.7e-291) || (!(d2 <= 1.5e-286) && ((d2 <= 2.6e-286) || (!(d2 <= 1.05e-285) && ((d2 <= 1.35e-284) || (!(d2 <= 1.8e-283) && ((d2 <= 5.8e-280) || (!(d2 <= 8.5e-232) && ((d2 <= 3.7e-215) || (!(d2 <= 2e-210) && ((d2 <= 4.5e-207) || (!(d2 <= 2.3e-191) && ((d2 <= 1.5e-169) || (!(d2 <= 3.4e-167) && ((d2 <= 2.55e-160) || (!(d2 <= 4.6e-159) && ((d2 <= 1.05e-134) || (!(d2 <= 3.2e-73) && (d2 <= 1.32e-64))))))))))))))))))))))))))))))))))))))))))))))) {
		tmp = d1 * 37.0;
	} else {
		tmp = d1 * d3;
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d2 <= -38.0:
		tmp = d1 * d2
	elif (d2 <= -1.25e-26) or (not (d2 <= -1.05e-36) and ((d2 <= -7.8e-41) or (not (d2 <= -3.4e-45) and ((d2 <= -1.5e-61) or (not (d2 <= -1e-64) and ((d2 <= -1.7e-81) or (not (d2 <= -1.7e-82) and ((d2 <= -3.9e-121) or (not (d2 <= -6.5e-136) and ((d2 <= -5.9e-140) or (not (d2 <= -1.05e-146) and ((d2 <= -2.55e-173) or (not (d2 <= -3.3e-190) and ((d2 <= -3.15e-198) or (not (d2 <= -1.2e-211) and ((d2 <= -3e-216) or (not (d2 <= -7.6e-226) and ((d2 <= -3.35e-239) or (not (d2 <= -1.75e-239) and ((d2 <= -1.2e-248) or (not (d2 <= -9.2e-253) and ((d2 <= -7.2e-258) or (not (d2 <= -1.3e-280) and ((d2 <= -9.8e-291) or (not (d2 <= -5.2e-301) and ((d2 <= -1.5e-306) or (not (d2 <= 2.4e-295) and ((d2 <= 3.7e-291) or (not (d2 <= 1.5e-286) and ((d2 <= 2.6e-286) or (not (d2 <= 1.05e-285) and ((d2 <= 1.35e-284) or (not (d2 <= 1.8e-283) and ((d2 <= 5.8e-280) or (not (d2 <= 8.5e-232) and ((d2 <= 3.7e-215) or (not (d2 <= 2e-210) and ((d2 <= 4.5e-207) or (not (d2 <= 2.3e-191) and ((d2 <= 1.5e-169) or (not (d2 <= 3.4e-167) and ((d2 <= 2.55e-160) or (not (d2 <= 4.6e-159) and ((d2 <= 1.05e-134) or (not (d2 <= 3.2e-73) and (d2 <= 1.32e-64)))))))))))))))))))))))))))))))))))))))))))))):
		tmp = d1 * 37.0
	else:
		tmp = d1 * d3
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d2 <= -38.0)
		tmp = Float64(d1 * d2);
	elseif ((d2 <= -1.25e-26) || (!(d2 <= -1.05e-36) && ((d2 <= -7.8e-41) || (!(d2 <= -3.4e-45) && ((d2 <= -1.5e-61) || (!(d2 <= -1e-64) && ((d2 <= -1.7e-81) || (!(d2 <= -1.7e-82) && ((d2 <= -3.9e-121) || (!(d2 <= -6.5e-136) && ((d2 <= -5.9e-140) || (!(d2 <= -1.05e-146) && ((d2 <= -2.55e-173) || (!(d2 <= -3.3e-190) && ((d2 <= -3.15e-198) || (!(d2 <= -1.2e-211) && ((d2 <= -3e-216) || (!(d2 <= -7.6e-226) && ((d2 <= -3.35e-239) || (!(d2 <= -1.75e-239) && ((d2 <= -1.2e-248) || (!(d2 <= -9.2e-253) && ((d2 <= -7.2e-258) || (!(d2 <= -1.3e-280) && ((d2 <= -9.8e-291) || (!(d2 <= -5.2e-301) && ((d2 <= -1.5e-306) || (!(d2 <= 2.4e-295) && ((d2 <= 3.7e-291) || (!(d2 <= 1.5e-286) && ((d2 <= 2.6e-286) || (!(d2 <= 1.05e-285) && ((d2 <= 1.35e-284) || (!(d2 <= 1.8e-283) && ((d2 <= 5.8e-280) || (!(d2 <= 8.5e-232) && ((d2 <= 3.7e-215) || (!(d2 <= 2e-210) && ((d2 <= 4.5e-207) || (!(d2 <= 2.3e-191) && ((d2 <= 1.5e-169) || (!(d2 <= 3.4e-167) && ((d2 <= 2.55e-160) || (!(d2 <= 4.6e-159) && ((d2 <= 1.05e-134) || (!(d2 <= 3.2e-73) && (d2 <= 1.32e-64)))))))))))))))))))))))))))))))))))))))))))))))
		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 <= -38.0)
		tmp = d1 * d2;
	elseif ((d2 <= -1.25e-26) || (~((d2 <= -1.05e-36)) && ((d2 <= -7.8e-41) || (~((d2 <= -3.4e-45)) && ((d2 <= -1.5e-61) || (~((d2 <= -1e-64)) && ((d2 <= -1.7e-81) || (~((d2 <= -1.7e-82)) && ((d2 <= -3.9e-121) || (~((d2 <= -6.5e-136)) && ((d2 <= -5.9e-140) || (~((d2 <= -1.05e-146)) && ((d2 <= -2.55e-173) || (~((d2 <= -3.3e-190)) && ((d2 <= -3.15e-198) || (~((d2 <= -1.2e-211)) && ((d2 <= -3e-216) || (~((d2 <= -7.6e-226)) && ((d2 <= -3.35e-239) || (~((d2 <= -1.75e-239)) && ((d2 <= -1.2e-248) || (~((d2 <= -9.2e-253)) && ((d2 <= -7.2e-258) || (~((d2 <= -1.3e-280)) && ((d2 <= -9.8e-291) || (~((d2 <= -5.2e-301)) && ((d2 <= -1.5e-306) || (~((d2 <= 2.4e-295)) && ((d2 <= 3.7e-291) || (~((d2 <= 1.5e-286)) && ((d2 <= 2.6e-286) || (~((d2 <= 1.05e-285)) && ((d2 <= 1.35e-284) || (~((d2 <= 1.8e-283)) && ((d2 <= 5.8e-280) || (~((d2 <= 8.5e-232)) && ((d2 <= 3.7e-215) || (~((d2 <= 2e-210)) && ((d2 <= 4.5e-207) || (~((d2 <= 2.3e-191)) && ((d2 <= 1.5e-169) || (~((d2 <= 3.4e-167)) && ((d2 <= 2.55e-160) || (~((d2 <= 4.6e-159)) && ((d2 <= 1.05e-134) || (~((d2 <= 3.2e-73)) && (d2 <= 1.32e-64)))))))))))))))))))))))))))))))))))))))))))))))
		tmp = d1 * 37.0;
	else
		tmp = d1 * d3;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d2, -38.0], N[(d1 * d2), $MachinePrecision], If[Or[LessEqual[d2, -1.25e-26], And[N[Not[LessEqual[d2, -1.05e-36]], $MachinePrecision], Or[LessEqual[d2, -7.8e-41], And[N[Not[LessEqual[d2, -3.4e-45]], $MachinePrecision], Or[LessEqual[d2, -1.5e-61], And[N[Not[LessEqual[d2, -1e-64]], $MachinePrecision], Or[LessEqual[d2, -1.7e-81], And[N[Not[LessEqual[d2, -1.7e-82]], $MachinePrecision], Or[LessEqual[d2, -3.9e-121], And[N[Not[LessEqual[d2, -6.5e-136]], $MachinePrecision], Or[LessEqual[d2, -5.9e-140], And[N[Not[LessEqual[d2, -1.05e-146]], $MachinePrecision], Or[LessEqual[d2, -2.55e-173], And[N[Not[LessEqual[d2, -3.3e-190]], $MachinePrecision], Or[LessEqual[d2, -3.15e-198], And[N[Not[LessEqual[d2, -1.2e-211]], $MachinePrecision], Or[LessEqual[d2, -3e-216], And[N[Not[LessEqual[d2, -7.6e-226]], $MachinePrecision], Or[LessEqual[d2, -3.35e-239], And[N[Not[LessEqual[d2, -1.75e-239]], $MachinePrecision], Or[LessEqual[d2, -1.2e-248], And[N[Not[LessEqual[d2, -9.2e-253]], $MachinePrecision], Or[LessEqual[d2, -7.2e-258], And[N[Not[LessEqual[d2, -1.3e-280]], $MachinePrecision], Or[LessEqual[d2, -9.8e-291], And[N[Not[LessEqual[d2, -5.2e-301]], $MachinePrecision], Or[LessEqual[d2, -1.5e-306], And[N[Not[LessEqual[d2, 2.4e-295]], $MachinePrecision], Or[LessEqual[d2, 3.7e-291], And[N[Not[LessEqual[d2, 1.5e-286]], $MachinePrecision], Or[LessEqual[d2, 2.6e-286], And[N[Not[LessEqual[d2, 1.05e-285]], $MachinePrecision], Or[LessEqual[d2, 1.35e-284], And[N[Not[LessEqual[d2, 1.8e-283]], $MachinePrecision], Or[LessEqual[d2, 5.8e-280], And[N[Not[LessEqual[d2, 8.5e-232]], $MachinePrecision], Or[LessEqual[d2, 3.7e-215], And[N[Not[LessEqual[d2, 2e-210]], $MachinePrecision], Or[LessEqual[d2, 4.5e-207], And[N[Not[LessEqual[d2, 2.3e-191]], $MachinePrecision], Or[LessEqual[d2, 1.5e-169], And[N[Not[LessEqual[d2, 3.4e-167]], $MachinePrecision], Or[LessEqual[d2, 2.55e-160], And[N[Not[LessEqual[d2, 4.6e-159]], $MachinePrecision], Or[LessEqual[d2, 1.05e-134], And[N[Not[LessEqual[d2, 3.2e-73]], $MachinePrecision], LessEqual[d2, 1.32e-64]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]], N[(d1 * 37.0), $MachinePrecision], N[(d1 * d3), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d2 < -38

   1. Initial program 94.3%

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

      1. cancel-sign-sub 94.3%

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

      2. +-commutative 94.3%

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

      3. *-commutative 94.3%

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

      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 76.2%

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

   if -38 < d2 < -1.25000000000000005e-26 or -1.04999999999999995e-36 < d2 < -7.79999999999999982e-41 or -3.40000000000000004e-45 < d2 < -1.50000000000000006e-61 or -9.99999999999999965e-65 < d2 < -1.6999999999999999e-81 or -1.69999999999999988e-82 < d2 < -3.9e-121 or -6.50000000000000011e-136 < d2 < -5.9000000000000002e-140 or -1.05e-146 < d2 < -2.5499999999999999e-173 or -3.30000000000000019e-190 < d2 < -3.15000000000000008e-198 or -1.2000000000000001e-211 < d2 < -3.00000000000000013e-216 or -7.59999999999999963e-226 < d2 < -3.35000000000000019e-239 or -1.75000000000000003e-239 < d2 < -1.20000000000000002e-248 or -9.2000000000000001e-253 < d2 < -7.19999999999999958e-258 or -1.3e-280 < d2 < -9.79999999999999988e-291 or -5.1999999999999996e-301 < d2 < -1.50000000000000012e-306 or 2.3999999999999998e-295 < d2 < 3.7000000000000001e-291 or 1.5e-286 < d2 < 2.6e-286 or 1.04999999999999992e-285 < d2 < 1.34999999999999992e-284 or 1.8e-283 < d2 < 5.8e-280 or 8.5e-232 < d2 < 3.70000000000000009e-215 or 2.0000000000000001e-210 < d2 < 4.49999999999999992e-207 or 2.30000000000000011e-191 < d2 < 1.5e-169 or 3.3999999999999997e-167 < d2 < 2.55e-160 or 4.59999999999999957e-159 < d2 < 1.05e-134 or 3.19999999999999986e-73 < d2 < 1.32e-64

   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-- 99.9%

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

      8. associate-+r+ 99.9%

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

      9. +-commutative 99.9%

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

      10. associate--l+ 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

      14. associate-+l+ 99.9%

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

      15. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in d2 around 0 99.9%

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

   6. Taylor expanded in d3 around 0 66.4%

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

      1. *-commutative 66.4%

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

   8. Simplified 66.4%

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

   if -1.25000000000000005e-26 < d2 < -1.04999999999999995e-36 or -7.79999999999999982e-41 < d2 < -3.40000000000000004e-45 or -1.50000000000000006e-61 < d2 < -9.99999999999999965e-65 or -1.6999999999999999e-81 < d2 < -1.69999999999999988e-82 or -3.9e-121 < d2 < -6.50000000000000011e-136 or -5.9000000000000002e-140 < d2 < -1.05e-146 or -2.5499999999999999e-173 < d2 < -3.30000000000000019e-190 or -3.15000000000000008e-198 < d2 < -1.2000000000000001e-211 or -3.00000000000000013e-216 < d2 < -7.59999999999999963e-226 or -3.35000000000000019e-239 < d2 < -1.75000000000000003e-239 or -1.20000000000000002e-248 < d2 < -9.2000000000000001e-253 or -7.19999999999999958e-258 < d2 < -1.3e-280 or -9.79999999999999988e-291 < d2 < -5.1999999999999996e-301 or -1.50000000000000012e-306 < d2 < 2.3999999999999998e-295 or 3.7000000000000001e-291 < d2 < 1.5e-286 or 2.6e-286 < d2 < 1.04999999999999992e-285 or 1.34999999999999992e-284 < d2 < 1.8e-283 or 5.8e-280 < d2 < 8.5e-232 or 3.70000000000000009e-215 < d2 < 2.0000000000000001e-210 or 4.49999999999999992e-207 < d2 < 2.30000000000000011e-191 or 1.5e-169 < d2 < 3.3999999999999997e-167 or 2.55e-160 < d2 < 4.59999999999999957e-159 or 1.05e-134 < d2 < 3.19999999999999986e-73 or 1.32e-64 < d2

   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 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 55.6%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -38:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d2 \leq -1.25 \cdot 10^{-26} \lor \neg \left(d2 \leq -1.05 \cdot 10^{-36}\right) \land \left(d2 \leq -7.8 \cdot 10^{-41} \lor \neg \left(d2 \leq -3.4 \cdot 10^{-45}\right) \land \left(d2 \leq -1.5 \cdot 10^{-61} \lor \neg \left(d2 \leq -1 \cdot 10^{-64}\right) \land \left(d2 \leq -1.7 \cdot 10^{-81} \lor \neg \left(d2 \leq -1.7 \cdot 10^{-82}\right) \land \left(d2 \leq -3.9 \cdot 10^{-121} \lor \neg \left(d2 \leq -6.5 \cdot 10^{-136}\right) \land \left(d2 \leq -5.9 \cdot 10^{-140} \lor \neg \left(d2 \leq -1.05 \cdot 10^{-146}\right) \land \left(d2 \leq -2.55 \cdot 10^{-173} \lor \neg \left(d2 \leq -3.3 \cdot 10^{-190}\right) \land \left(d2 \leq -3.15 \cdot 10^{-198} \lor \neg \left(d2 \leq -1.2 \cdot 10^{-211}\right) \land \left(d2 \leq -3 \cdot 10^{-216} \lor \neg \left(d2 \leq -7.6 \cdot 10^{-226}\right) \land \left(d2 \leq -3.35 \cdot 10^{-239} \lor \neg \left(d2 \leq -1.75 \cdot 10^{-239}\right) \land \left(d2 \leq -1.2 \cdot 10^{-248} \lor \neg \left(d2 \leq -9.2 \cdot 10^{-253}\right) \land \left(d2 \leq -7.2 \cdot 10^{-258} \lor \neg \left(d2 \leq -1.3 \cdot 10^{-280}\right) \land \left(d2 \leq -9.8 \cdot 10^{-291} \lor \neg \left(d2 \leq -5.2 \cdot 10^{-301}\right) \land \left(d2 \leq -1.5 \cdot 10^{-306} \lor \neg \left(d2 \leq 2.4 \cdot 10^{-295}\right) \land \left(d2 \leq 3.7 \cdot 10^{-291} \lor \neg \left(d2 \leq 1.5 \cdot 10^{-286}\right) \land \left(d2 \leq 2.6 \cdot 10^{-286} \lor \neg \left(d2 \leq 1.05 \cdot 10^{-285}\right) \land \left(d2 \leq 1.35 \cdot 10^{-284} \lor \neg \left(d2 \leq 1.8 \cdot 10^{-283}\right) \land \left(d2 \leq 5.8 \cdot 10^{-280} \lor \neg \left(d2 \leq 8.5 \cdot 10^{-232}\right) \land \left(d2 \leq 3.7 \cdot 10^{-215} \lor \neg \left(d2 \leq 2 \cdot 10^{-210}\right) \land \left(d2 \leq 4.5 \cdot 10^{-207} \lor \neg \left(d2 \leq 2.3 \cdot 10^{-191}\right) \land \left(d2 \leq 1.5 \cdot 10^{-169} \lor \neg \left(d2 \leq 3.4 \cdot 10^{-167}\right) \land \left(d2 \leq 2.55 \cdot 10^{-160} \lor \neg \left(d2 \leq 4.6 \cdot 10^{-159}\right) \land \left(d2 \leq 1.05 \cdot 10^{-134} \lor \neg \left(d2 \leq 3.2 \cdot 10^{-73}\right) \land d2 \leq 1.32 \cdot 10^{-64}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right):\\ \;\;\;\;d1 \cdot 37\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d3\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := d1 \cdot \left(d2 + 37\right)\\ \mathbf{if}\;d3 \leq 1150000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d3 \leq 1.4 \cdot 10^{+39}:\\ \;\;\;\;d1 \cdot d3\\ \mathbf{elif}\;d3 \leq 7 \cdot 10^{+40}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;d3 \leq 1.35 \cdot 10^{+41} \lor \neg \left(d3 \leq 4.8 \cdot 10^{+44}\right) \land \left(d3 \leq 9 \cdot 10^{+62} \lor \neg \left(d3 \leq 4.4 \cdot 10^{+63}\right) \land \left(d3 \leq 9 \cdot 10^{+87} \lor \neg \left(d3 \leq 1.5 \cdot 10^{+88}\right) \land \left(d3 \leq 9.2 \cdot 10^{+109} \lor \neg \left(d3 \leq 10^{+112}\right) \land \left(d3 \leq 6.2 \cdot 10^{+119} \lor \neg \left(d3 \leq 1.3 \cdot 10^{+131}\right) \land \left(d3 \leq 3.4 \cdot 10^{+139} \lor \neg \left(d3 \leq 1.82 \cdot 10^{+140}\right) \land \left(d3 \leq 2.1 \cdot 10^{+156} \lor \neg \left(d3 \leq 3.2 \cdot 10^{+156}\right) \land \left(d3 \leq 1.25 \cdot 10^{+184} \lor \neg \left(d3 \leq 2.15 \cdot 10^{+187}\right) \land \left(d3 \leq 4.1 \cdot 10^{+220} \lor \neg \left(d3 \leq 4.2 \cdot 10^{+220}\right) \land \left(d3 \leq 1.3 \cdot 10^{+231} \lor \neg \left(d3 \leq 1.35 \cdot 10^{+231}\right) \land \left(d3 \leq 1.6 \cdot 10^{+235} \lor \neg \left(d3 \leq 1.65 \cdot 10^{+235}\right) \land \left(d3 \leq 1.05 \cdot 10^{+270} \lor \neg \left(d3 \leq 1.1 \cdot 10^{+270}\right) \land \left(d3 \leq 3.5 \cdot 10^{+283} \lor \neg \left(d3 \leq 3.6 \cdot 10^{+283}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right):\\ \;\;\;\;d1 \cdot d3\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d2\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (let* ((t_0 (* d1 (+ d2 37.0))))
   (if (<= d3 1150000.0)
     t_0
     (if (<= d3 1.4e+39)
       (* d1 d3)
       (if (<= d3 7e+40)
         t_0
         (if (or (<= d3 1.35e+41)
                 (and (not (<= d3 4.8e+44))
                      (or (<= d3 9e+62)
                          (and (not (<= d3 4.4e+63))
                               (or (<= d3 9e+87)
                                   (and (not (<= d3 1.5e+88))
                                        (or (<= d3 9.2e+109)
                                            (and (not (<= d3 1e+112))
                                                 (or (<= d3 6.2e+119)
                                                     (and (not
                                                           (<= d3 1.3e+131))
                                                          (or (<= d3 3.4e+139)
                                                              (and (not
                                                                    (<=
                                                                     d3
                                                                     1.82e+140))
                                                                   (or (<=
                                                                        d3
                                                                        2.1e+156)
                                                                       (and (not
                                                                             (<=
                                                                              d3
                                                                              3.2e+156))
                                                                            (or (<=
                                                                                 d3
                                                                                 1.25e+184)
                                                                                (and (not
                                                                                      (<=
                                                                                       d3
                                                                                       2.15e+187))
                                                                                     (or (<=
                                                                                          d3
                                                                                          4.1e+220)
                                                                                         (and (not
                                                                                               (<=
                                                                                                d3
                                                                                                4.2e+220))
                                                                                              (or (<=
                                                                                                   d3
                                                                                                   1.3e+231)
                                                                                                  (and (not
                                                                                                        (<=
                                                                                                         d3
                                                                                                         1.35e+231))
                                                                                                       (or (<=
                                                                                                            d3
                                                                                                            1.6e+235)
                                                                                                           (and (not
                                                                                                                 (<=
                                                                                                                  d3
                                                                                                                  1.65e+235))
                                                                                                                (or (<=
                                                                                                                     d3
                                                                                                                     1.05e+270)
                                                                                                                    (and (not
                                                                                                                          (<=
                                                                                                                           d3
                                                                                                                           1.1e+270))
                                                                                                                         (or (<=
                                                                                                                              d3
                                                                                                                              3.5e+283)
                                                                                                                             (not
                                                                                                                              (<=
                                                                                                                               d3
                                                                                                                               3.6e+283)))))))))))))))))))))))))))
           (* d1 d3)
           (* d1 d2)))))))

C

double code(double d1, double d2, double d3) {
	double t_0 = d1 * (d2 + 37.0);
	double tmp;
	if (d3 <= 1150000.0) {
		tmp = t_0;
	} else if (d3 <= 1.4e+39) {
		tmp = d1 * d3;
	} else if (d3 <= 7e+40) {
		tmp = t_0;
	} else if ((d3 <= 1.35e+41) || (!(d3 <= 4.8e+44) && ((d3 <= 9e+62) || (!(d3 <= 4.4e+63) && ((d3 <= 9e+87) || (!(d3 <= 1.5e+88) && ((d3 <= 9.2e+109) || (!(d3 <= 1e+112) && ((d3 <= 6.2e+119) || (!(d3 <= 1.3e+131) && ((d3 <= 3.4e+139) || (!(d3 <= 1.82e+140) && ((d3 <= 2.1e+156) || (!(d3 <= 3.2e+156) && ((d3 <= 1.25e+184) || (!(d3 <= 2.15e+187) && ((d3 <= 4.1e+220) || (!(d3 <= 4.2e+220) && ((d3 <= 1.3e+231) || (!(d3 <= 1.35e+231) && ((d3 <= 1.6e+235) || (!(d3 <= 1.65e+235) && ((d3 <= 1.05e+270) || (!(d3 <= 1.1e+270) && ((d3 <= 3.5e+283) || !(d3 <= 3.6e+283)))))))))))))))))))))))))) {
		tmp = d1 * d3;
	} else {
		tmp = d1 * d2;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = d1 * (d2 + 37.0d0)
    if (d3 <= 1150000.0d0) then
        tmp = t_0
    else if (d3 <= 1.4d+39) then
        tmp = d1 * d3
    else if (d3 <= 7d+40) then
        tmp = t_0
    else if ((d3 <= 1.35d+41) .or. (.not. (d3 <= 4.8d+44)) .and. (d3 <= 9d+62) .or. (.not. (d3 <= 4.4d+63)) .and. (d3 <= 9d+87) .or. (.not. (d3 <= 1.5d+88)) .and. (d3 <= 9.2d+109) .or. (.not. (d3 <= 1d+112)) .and. (d3 <= 6.2d+119) .or. (.not. (d3 <= 1.3d+131)) .and. (d3 <= 3.4d+139) .or. (.not. (d3 <= 1.82d+140)) .and. (d3 <= 2.1d+156) .or. (.not. (d3 <= 3.2d+156)) .and. (d3 <= 1.25d+184) .or. (.not. (d3 <= 2.15d+187)) .and. (d3 <= 4.1d+220) .or. (.not. (d3 <= 4.2d+220)) .and. (d3 <= 1.3d+231) .or. (.not. (d3 <= 1.35d+231)) .and. (d3 <= 1.6d+235) .or. (.not. (d3 <= 1.65d+235)) .and. (d3 <= 1.05d+270) .or. (.not. (d3 <= 1.1d+270)) .and. (d3 <= 3.5d+283) .or. (.not. (d3 <= 3.6d+283))) then
        tmp = d1 * d3
    else
        tmp = d1 * d2
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3) {
	double t_0 = d1 * (d2 + 37.0);
	double tmp;
	if (d3 <= 1150000.0) {
		tmp = t_0;
	} else if (d3 <= 1.4e+39) {
		tmp = d1 * d3;
	} else if (d3 <= 7e+40) {
		tmp = t_0;
	} else if ((d3 <= 1.35e+41) || (!(d3 <= 4.8e+44) && ((d3 <= 9e+62) || (!(d3 <= 4.4e+63) && ((d3 <= 9e+87) || (!(d3 <= 1.5e+88) && ((d3 <= 9.2e+109) || (!(d3 <= 1e+112) && ((d3 <= 6.2e+119) || (!(d3 <= 1.3e+131) && ((d3 <= 3.4e+139) || (!(d3 <= 1.82e+140) && ((d3 <= 2.1e+156) || (!(d3 <= 3.2e+156) && ((d3 <= 1.25e+184) || (!(d3 <= 2.15e+187) && ((d3 <= 4.1e+220) || (!(d3 <= 4.2e+220) && ((d3 <= 1.3e+231) || (!(d3 <= 1.35e+231) && ((d3 <= 1.6e+235) || (!(d3 <= 1.65e+235) && ((d3 <= 1.05e+270) || (!(d3 <= 1.1e+270) && ((d3 <= 3.5e+283) || !(d3 <= 3.6e+283)))))))))))))))))))))))))) {
		tmp = d1 * d3;
	} else {
		tmp = d1 * d2;
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	t_0 = d1 * (d2 + 37.0)
	tmp = 0
	if d3 <= 1150000.0:
		tmp = t_0
	elif d3 <= 1.4e+39:
		tmp = d1 * d3
	elif d3 <= 7e+40:
		tmp = t_0
	elif (d3 <= 1.35e+41) or (not (d3 <= 4.8e+44) and ((d3 <= 9e+62) or (not (d3 <= 4.4e+63) and ((d3 <= 9e+87) or (not (d3 <= 1.5e+88) and ((d3 <= 9.2e+109) or (not (d3 <= 1e+112) and ((d3 <= 6.2e+119) or (not (d3 <= 1.3e+131) and ((d3 <= 3.4e+139) or (not (d3 <= 1.82e+140) and ((d3 <= 2.1e+156) or (not (d3 <= 3.2e+156) and ((d3 <= 1.25e+184) or (not (d3 <= 2.15e+187) and ((d3 <= 4.1e+220) or (not (d3 <= 4.2e+220) and ((d3 <= 1.3e+231) or (not (d3 <= 1.35e+231) and ((d3 <= 1.6e+235) or (not (d3 <= 1.65e+235) and ((d3 <= 1.05e+270) or (not (d3 <= 1.1e+270) and ((d3 <= 3.5e+283) or not (d3 <= 3.6e+283))))))))))))))))))))))))):
		tmp = d1 * d3
	else:
		tmp = d1 * d2
	return tmp

Julia

function code(d1, d2, d3)
	t_0 = Float64(d1 * Float64(d2 + 37.0))
	tmp = 0.0
	if (d3 <= 1150000.0)
		tmp = t_0;
	elseif (d3 <= 1.4e+39)
		tmp = Float64(d1 * d3);
	elseif (d3 <= 7e+40)
		tmp = t_0;
	elseif ((d3 <= 1.35e+41) || (!(d3 <= 4.8e+44) && ((d3 <= 9e+62) || (!(d3 <= 4.4e+63) && ((d3 <= 9e+87) || (!(d3 <= 1.5e+88) && ((d3 <= 9.2e+109) || (!(d3 <= 1e+112) && ((d3 <= 6.2e+119) || (!(d3 <= 1.3e+131) && ((d3 <= 3.4e+139) || (!(d3 <= 1.82e+140) && ((d3 <= 2.1e+156) || (!(d3 <= 3.2e+156) && ((d3 <= 1.25e+184) || (!(d3 <= 2.15e+187) && ((d3 <= 4.1e+220) || (!(d3 <= 4.2e+220) && ((d3 <= 1.3e+231) || (!(d3 <= 1.35e+231) && ((d3 <= 1.6e+235) || (!(d3 <= 1.65e+235) && ((d3 <= 1.05e+270) || (!(d3 <= 1.1e+270) && ((d3 <= 3.5e+283) || !(d3 <= 3.6e+283))))))))))))))))))))))))))
		tmp = Float64(d1 * d3);
	else
		tmp = Float64(d1 * d2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3)
	t_0 = d1 * (d2 + 37.0);
	tmp = 0.0;
	if (d3 <= 1150000.0)
		tmp = t_0;
	elseif (d3 <= 1.4e+39)
		tmp = d1 * d3;
	elseif (d3 <= 7e+40)
		tmp = t_0;
	elseif ((d3 <= 1.35e+41) || (~((d3 <= 4.8e+44)) && ((d3 <= 9e+62) || (~((d3 <= 4.4e+63)) && ((d3 <= 9e+87) || (~((d3 <= 1.5e+88)) && ((d3 <= 9.2e+109) || (~((d3 <= 1e+112)) && ((d3 <= 6.2e+119) || (~((d3 <= 1.3e+131)) && ((d3 <= 3.4e+139) || (~((d3 <= 1.82e+140)) && ((d3 <= 2.1e+156) || (~((d3 <= 3.2e+156)) && ((d3 <= 1.25e+184) || (~((d3 <= 2.15e+187)) && ((d3 <= 4.1e+220) || (~((d3 <= 4.2e+220)) && ((d3 <= 1.3e+231) || (~((d3 <= 1.35e+231)) && ((d3 <= 1.6e+235) || (~((d3 <= 1.65e+235)) && ((d3 <= 1.05e+270) || (~((d3 <= 1.1e+270)) && ((d3 <= 3.5e+283) || ~((d3 <= 3.6e+283)))))))))))))))))))))))))))
		tmp = d1 * d3;
	else
		tmp = d1 * d2;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := Block[{t$95$0 = N[(d1 * N[(d2 + 37.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d3, 1150000.0], t$95$0, If[LessEqual[d3, 1.4e+39], N[(d1 * d3), $MachinePrecision], If[LessEqual[d3, 7e+40], t$95$0, If[Or[LessEqual[d3, 1.35e+41], And[N[Not[LessEqual[d3, 4.8e+44]], $MachinePrecision], Or[LessEqual[d3, 9e+62], And[N[Not[LessEqual[d3, 4.4e+63]], $MachinePrecision], Or[LessEqual[d3, 9e+87], And[N[Not[LessEqual[d3, 1.5e+88]], $MachinePrecision], Or[LessEqual[d3, 9.2e+109], And[N[Not[LessEqual[d3, 1e+112]], $MachinePrecision], Or[LessEqual[d3, 6.2e+119], And[N[Not[LessEqual[d3, 1.3e+131]], $MachinePrecision], Or[LessEqual[d3, 3.4e+139], And[N[Not[LessEqual[d3, 1.82e+140]], $MachinePrecision], Or[LessEqual[d3, 2.1e+156], And[N[Not[LessEqual[d3, 3.2e+156]], $MachinePrecision], Or[LessEqual[d3, 1.25e+184], And[N[Not[LessEqual[d3, 2.15e+187]], $MachinePrecision], Or[LessEqual[d3, 4.1e+220], And[N[Not[LessEqual[d3, 4.2e+220]], $MachinePrecision], Or[LessEqual[d3, 1.3e+231], And[N[Not[LessEqual[d3, 1.35e+231]], $MachinePrecision], Or[LessEqual[d3, 1.6e+235], And[N[Not[LessEqual[d3, 1.65e+235]], $MachinePrecision], Or[LessEqual[d3, 1.05e+270], And[N[Not[LessEqual[d3, 1.1e+270]], $MachinePrecision], Or[LessEqual[d3, 3.5e+283], N[Not[LessEqual[d3, 3.6e+283]], $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]]], N[(d1 * d3), $MachinePrecision], N[(d1 * d2), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if d3 < 1.15e6 or 1.40000000000000001e39 < d3 < 6.9999999999999998e40

   1. Initial program 96.3%

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

      1. cancel-sign-sub 96.3%

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

      2. +-commutative 96.3%

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

      3. *-commutative 96.3%

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

      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-- 99.9%

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

      8. associate-+r+ 99.9%

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

      9. +-commutative 99.9%

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

      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 69.7%

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

   if 1.15e6 < d3 < 1.40000000000000001e39 or 6.9999999999999998e40 < d3 < 1.35e41 or 4.80000000000000026e44 < d3 < 8.99999999999999997e62 or 4.3999999999999997e63 < d3 < 9.0000000000000005e87 or 1.50000000000000003e88 < d3 < 9.20000000000000042e109 or 9.9999999999999993e111 < d3 < 6.1999999999999999e119 or 1.3e131 < d3 < 3.4000000000000002e139 or 1.82e140 < d3 < 2.09999999999999981e156 or 3.20000000000000002e156 < d3 < 1.25e184 or 2.1499999999999999e187 < d3 < 4.09999999999999981e220 or 4.20000000000000014e220 < d3 < 1.2999999999999999e231 or 1.35e231 < d3 < 1.60000000000000003e235 or 1.65e235 < d3 < 1.05000000000000005e270 or 1.10000000000000005e270 < d3 < 3.49999999999999995e283 or 3.60000000000000017e283 < d3

   1. Initial program 98.1%

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

      1. cancel-sign-sub 98.1%

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

      2. +-commutative 98.1%

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

      3. *-commutative 98.1%

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

      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 83.6%

      \[\leadsto \color{blue}{d1 \cdot d3} \]

   if 1.35e41 < d3 < 4.80000000000000026e44 or 8.99999999999999997e62 < d3 < 4.3999999999999997e63 or 9.0000000000000005e87 < d3 < 1.50000000000000003e88 or 9.20000000000000042e109 < d3 < 9.9999999999999993e111 or 6.1999999999999999e119 < d3 < 1.3e131 or 3.4000000000000002e139 < d3 < 1.82e140 or 2.09999999999999981e156 < d3 < 3.20000000000000002e156 or 1.25e184 < d3 < 2.1499999999999999e187 or 4.09999999999999981e220 < d3 < 4.20000000000000014e220 or 1.2999999999999999e231 < d3 < 1.35e231 or 1.60000000000000003e235 < d3 < 1.65e235 or 1.05000000000000005e270 < d3 < 1.10000000000000005e270 or 3.49999999999999995e283 < d3 < 3.60000000000000017e283

   1. Initial program 75.0%

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

      1. cancel-sign-sub 75.0%

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

      2. +-commutative 75.0%

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

      3. *-commutative 75.0%

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

      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 d2 around inf 98.4%

      \[\leadsto \color{blue}{d1 \cdot d2} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq 1150000:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{elif}\;d3 \leq 1.4 \cdot 10^{+39}:\\ \;\;\;\;d1 \cdot d3\\ \mathbf{elif}\;d3 \leq 7 \cdot 10^{+40}:\\ \;\;\;\;d1 \cdot \left(d2 + 37\right)\\ \mathbf{elif}\;d3 \leq 1.35 \cdot 10^{+41} \lor \neg \left(d3 \leq 4.8 \cdot 10^{+44}\right) \land \left(d3 \leq 9 \cdot 10^{+62} \lor \neg \left(d3 \leq 4.4 \cdot 10^{+63}\right) \land \left(d3 \leq 9 \cdot 10^{+87} \lor \neg \left(d3 \leq 1.5 \cdot 10^{+88}\right) \land \left(d3 \leq 9.2 \cdot 10^{+109} \lor \neg \left(d3 \leq 10^{+112}\right) \land \left(d3 \leq 6.2 \cdot 10^{+119} \lor \neg \left(d3 \leq 1.3 \cdot 10^{+131}\right) \land \left(d3 \leq 3.4 \cdot 10^{+139} \lor \neg \left(d3 \leq 1.82 \cdot 10^{+140}\right) \land \left(d3 \leq 2.1 \cdot 10^{+156} \lor \neg \left(d3 \leq 3.2 \cdot 10^{+156}\right) \land \left(d3 \leq 1.25 \cdot 10^{+184} \lor \neg \left(d3 \leq 2.15 \cdot 10^{+187}\right) \land \left(d3 \leq 4.1 \cdot 10^{+220} \lor \neg \left(d3 \leq 4.2 \cdot 10^{+220}\right) \land \left(d3 \leq 1.3 \cdot 10^{+231} \lor \neg \left(d3 \leq 1.35 \cdot 10^{+231}\right) \land \left(d3 \leq 1.6 \cdot 10^{+235} \lor \neg \left(d3 \leq 1.65 \cdot 10^{+235}\right) \land \left(d3 \leq 1.05 \cdot 10^{+270} \lor \neg \left(d3 \leq 1.1 \cdot 10^{+270}\right) \land \left(d3 \leq 3.5 \cdot 10^{+283} \lor \neg \left(d3 \leq 3.6 \cdot 10^{+283}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right):\\ \;\;\;\;d1 \cdot d3\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -38 \lor \neg \left(d2 \leq 37\right):\\ \;\;\;\;d1 \cdot d2\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot 37\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (or (<= d2 -38.0) (not (<= d2 37.0))) (* d1 d2) (* d1 37.0)))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if ((d2 <= -38.0) || !(d2 <= 37.0)) {
		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 <= (-38.0d0)) .or. (.not. (d2 <= 37.0d0))) 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 <= -38.0) || !(d2 <= 37.0)) {
		tmp = d1 * d2;
	} else {
		tmp = d1 * 37.0;
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if (d2 <= -38.0) or not (d2 <= 37.0):
		tmp = d1 * d2
	else:
		tmp = d1 * 37.0
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if ((d2 <= -38.0) || !(d2 <= 37.0))
		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 <= -38.0) || ~((d2 <= 37.0)))
		tmp = d1 * d2;
	else
		tmp = d1 * 37.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[Or[LessEqual[d2, -38.0], N[Not[LessEqual[d2, 37.0]], $MachinePrecision]], N[(d1 * d2), $MachinePrecision], N[(d1 * 37.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -38 or 37 < d2

   1. Initial program 91.7%

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

      1. cancel-sign-sub 91.7%

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

      2. +-commutative 91.7%

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

      3. *-commutative 91.7%

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

      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 73.8%

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

   if -38 < d2 < 37

   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-- 99.9%

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

      8. associate-+r+ 99.9%

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

      9. +-commutative 99.9%

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

      10. associate--l+ 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

      14. associate-+l+ 99.9%

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

      15. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in d2 around 0 99.1%

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

   6. Taylor expanded in d3 around 0 44.2%

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

      1. *-commutative 44.2%

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

   8. Simplified 44.2%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -38 \lor \neg \left(d2 \leq 37\right):\\ \;\;\;\;d1 \cdot d2\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot 37\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -2.4 \cdot 10^{+15}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d3 + 37\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3)
 :precision binary64
 (if (<= d2 -2.4e+15) (* d1 d2) (* d1 (+ d3 37.0))))

C

double code(double d1, double d2, double d3) {
	double tmp;
	if (d2 <= -2.4e+15) {
		tmp = d1 * d2;
	} 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 <= (-2.4d+15)) then
        tmp = d1 * d2
    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 <= -2.4e+15) {
		tmp = d1 * d2;
	} else {
		tmp = d1 * (d3 + 37.0);
	}
	return tmp;
}

Python

def code(d1, d2, d3):
	tmp = 0
	if d2 <= -2.4e+15:
		tmp = d1 * d2
	else:
		tmp = d1 * (d3 + 37.0)
	return tmp

Julia

function code(d1, d2, d3)
	tmp = 0.0
	if (d2 <= -2.4e+15)
		tmp = Float64(d1 * d2);
	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 <= -2.4e+15)
		tmp = d1 * d2;
	else
		tmp = d1 * (d3 + 37.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_] := If[LessEqual[d2, -2.4e+15], N[(d1 * d2), $MachinePrecision], N[(d1 * N[(d3 + 37.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -2.4e15

   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 d2 around inf 76.6%

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

   if -2.4e15 < d2

   1. Initial program 96.2%

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

      1. cancel-sign-sub 96.2%

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

      2. +-commutative 96.2%

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

      3. *-commutative 96.2%

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

      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-- 99.9%

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

      8. associate-+r+ 99.9%

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

      9. +-commutative 99.9%

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

      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 76.9%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -2.4 \cdot 10^{+15}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d3 + 37\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 26.7% 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 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 0 62.9%

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

6. Taylor expanded in d3 around 0 23.0%

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

   1. *-commutative 23.0%

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

8. Simplified 23.0%

   \[\leadsto \color{blue}{d1 \cdot 37} \]
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 2024096 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  :precision binary64

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

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