FastMath dist4

Percentage Accurate: 87.9% → 100.0%

Time: 9.8s

Alternatives: 14

Speedup: 1.7×

• 33.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)))

C

double code(double d1, double d2, double d3, double d4) {
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    code = (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
}

Python

def code(d1, d2, d3, d4):
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)

Julia

function code(d1, d2, d3, d4)
	return Float64(Float64(Float64(Float64(d1 * d2) - Float64(d1 * d3)) + Float64(d4 * d1)) - Float64(d1 * d1))
end

MATLAB

function tmp = code(d1, d2, d3, d4)
	tmp = (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
end

Wolfram

code[d1_, d2_, d3_, d4_] := N[(N[(N[(N[(d1 * d2), $MachinePrecision] - N[(d1 * d3), $MachinePrecision]), $MachinePrecision] + N[(d4 * d1), $MachinePrecision]), $MachinePrecision] - N[(d1 * d1), $MachinePrecision]), $MachinePrecision]

Initial Program: 87.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)))

C

double code(double d1, double d2, double d3, double d4) {
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    code = (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
}

Python

def code(d1, d2, d3, d4):
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)

Julia

function code(d1, d2, d3, d4)
	return Float64(Float64(Float64(Float64(d1 * d2) - Float64(d1 * d3)) + Float64(d4 * d1)) - Float64(d1 * d1))
end

MATLAB

function tmp = code(d1, d2, d3, d4)
	tmp = (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
end

Wolfram

code[d1_, d2_, d3_, d4_] := N[(N[(N[(N[(d1 * d2), $MachinePrecision] - N[(d1 * d3), $MachinePrecision]), $MachinePrecision] + N[(d4 * d1), $MachinePrecision]), $MachinePrecision] - N[(d1 * d1), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ d1 \cdot \left(\left(d2 + \left(d4 - d1\right)\right) - d3\right) \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4) :precision binary64 (* d1 (- (+ d2 (- d4 d1)) d3)))

C

double code(double d1, double d2, double d3, double d4) {
	return d1 * ((d2 + (d4 - d1)) - d3);
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    code = d1 * ((d2 + (d4 - d1)) - d3)
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	return d1 * ((d2 + (d4 - d1)) - d3);
}

Python

def code(d1, d2, d3, d4):
	return d1 * ((d2 + (d4 - d1)) - d3)

Julia

function code(d1, d2, d3, d4)
	return Float64(d1 * Float64(Float64(d2 + Float64(d4 - d1)) - d3))
end

MATLAB

function tmp = code(d1, d2, d3, d4)
	tmp = d1 * ((d2 + (d4 - d1)) - d3);
end

Wolfram

code[d1_, d2_, d3_, d4_] := N[(d1 * N[(N[(d2 + N[(d4 - d1), $MachinePrecision]), $MachinePrecision] - d3), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.4%

   \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
2. Step-by-step derivation

   1. +-commutative 84.4%

      \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

   2. *-commutative 84.4%

      \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

   3. distribute-lft-out-- 85.9%

      \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

   4. distribute-lft-out 89.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

   5. distribute-lft-out-- 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

   6. +-commutative 100.0%

      \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

   7. associate-+l- 100.0%

      \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

   8. associate--l- 100.0%

      \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

   9. associate--r- 100.0%

      \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

   10. sub-neg 100.0%

       \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

   11. sub-neg 100.0%

       \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

   12. +-commutative 100.0%

       \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

   13. distribute-neg-out 100.0%

       \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

   14. remove-double-neg 100.0%

       \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

   15. sub-neg 100.0%

       \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

   16. +-commutative 100.0%

       \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

   17. associate--l- 100.0%

       \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

4. Final simplification 100.0%

   \[\leadsto d1 \cdot \left(\left(d2 + \left(d4 - d1\right)\right) - d3\right) \]

Alternative 2: 63.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := d1 \cdot \left(-d1\right)\\ t_1 := d1 \cdot \left(-d3\right)\\ t_2 := d1 \cdot \left(d2 + d4\right)\\ \mathbf{if}\;d3 \leq -5.9 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d3 \leq -9 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;d3 \leq -3.2 \cdot 10^{-47}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d3 \leq 1.1 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;d3 \leq 7 \cdot 10^{+110}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d3 \leq 3.05 \cdot 10^{+172}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (* d1 (- d1))) (t_1 (* d1 (- d3))) (t_2 (* d1 (+ d2 d4))))
   (if (<= d3 -5.9e+141)
     t_1
     (if (<= d3 -9e+65)
       t_2
       (if (<= d3 -3.2e-47)
         t_0
         (if (<= d3 1.1e+38)
           t_2
           (if (<= d3 7e+110) t_0 (if (<= d3 3.05e+172) t_2 t_1))))))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * -d1;
	double t_1 = d1 * -d3;
	double t_2 = d1 * (d2 + d4);
	double tmp;
	if (d3 <= -5.9e+141) {
		tmp = t_1;
	} else if (d3 <= -9e+65) {
		tmp = t_2;
	} else if (d3 <= -3.2e-47) {
		tmp = t_0;
	} else if (d3 <= 1.1e+38) {
		tmp = t_2;
	} else if (d3 <= 7e+110) {
		tmp = t_0;
	} else if (d3 <= 3.05e+172) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = d1 * -d1
    t_1 = d1 * -d3
    t_2 = d1 * (d2 + d4)
    if (d3 <= (-5.9d+141)) then
        tmp = t_1
    else if (d3 <= (-9d+65)) then
        tmp = t_2
    else if (d3 <= (-3.2d-47)) then
        tmp = t_0
    else if (d3 <= 1.1d+38) then
        tmp = t_2
    else if (d3 <= 7d+110) then
        tmp = t_0
    else if (d3 <= 3.05d+172) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * -d1;
	double t_1 = d1 * -d3;
	double t_2 = d1 * (d2 + d4);
	double tmp;
	if (d3 <= -5.9e+141) {
		tmp = t_1;
	} else if (d3 <= -9e+65) {
		tmp = t_2;
	} else if (d3 <= -3.2e-47) {
		tmp = t_0;
	} else if (d3 <= 1.1e+38) {
		tmp = t_2;
	} else if (d3 <= 7e+110) {
		tmp = t_0;
	} else if (d3 <= 3.05e+172) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = d1 * -d1
	t_1 = d1 * -d3
	t_2 = d1 * (d2 + d4)
	tmp = 0
	if d3 <= -5.9e+141:
		tmp = t_1
	elif d3 <= -9e+65:
		tmp = t_2
	elif d3 <= -3.2e-47:
		tmp = t_0
	elif d3 <= 1.1e+38:
		tmp = t_2
	elif d3 <= 7e+110:
		tmp = t_0
	elif d3 <= 3.05e+172:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(d1 * Float64(-d1))
	t_1 = Float64(d1 * Float64(-d3))
	t_2 = Float64(d1 * Float64(d2 + d4))
	tmp = 0.0
	if (d3 <= -5.9e+141)
		tmp = t_1;
	elseif (d3 <= -9e+65)
		tmp = t_2;
	elseif (d3 <= -3.2e-47)
		tmp = t_0;
	elseif (d3 <= 1.1e+38)
		tmp = t_2;
	elseif (d3 <= 7e+110)
		tmp = t_0;
	elseif (d3 <= 3.05e+172)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	t_0 = d1 * -d1;
	t_1 = d1 * -d3;
	t_2 = d1 * (d2 + d4);
	tmp = 0.0;
	if (d3 <= -5.9e+141)
		tmp = t_1;
	elseif (d3 <= -9e+65)
		tmp = t_2;
	elseif (d3 <= -3.2e-47)
		tmp = t_0;
	elseif (d3 <= 1.1e+38)
		tmp = t_2;
	elseif (d3 <= 7e+110)
		tmp = t_0;
	elseif (d3 <= 3.05e+172)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := Block[{t$95$0 = N[(d1 * (-d1)), $MachinePrecision]}, Block[{t$95$1 = N[(d1 * (-d3)), $MachinePrecision]}, Block[{t$95$2 = N[(d1 * N[(d2 + d4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d3, -5.9e+141], t$95$1, If[LessEqual[d3, -9e+65], t$95$2, If[LessEqual[d3, -3.2e-47], t$95$0, If[LessEqual[d3, 1.1e+38], t$95$2, If[LessEqual[d3, 7e+110], t$95$0, If[LessEqual[d3, 3.05e+172], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if d3 < -5.90000000000000029e141 or 3.0499999999999999e172 < d3

   1. Initial program 81.5%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 81.5%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 81.5%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 84.6%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 89.2%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 99.9%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 99.9%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 99.9%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d3 around inf 81.7%

      \[\leadsto \color{blue}{-1 \cdot \left(d1 \cdot d3\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 81.7%

         \[\leadsto \color{blue}{\left(-1 \cdot d1\right) \cdot d3} \]

      2. neg-mul-1 81.7%

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

   6. Simplified 81.7%

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

   if -5.90000000000000029e141 < d3 < -9e65 or -3.1999999999999999e-47 < d3 < 1.10000000000000003e38 or 6.9999999999999998e110 < d3 < 3.0499999999999999e172

   1. Initial program 87.4%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 87.4%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 87.4%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 88.0%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 91.2%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 100.0%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d3 around 0 92.4%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d1\right)} \]

   5. Taylor expanded in d1 around 0 70.2%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + d4\right)} \]

   if -9e65 < d3 < -3.1999999999999999e-47 or 1.10000000000000003e38 < d3 < 6.9999999999999998e110

   1. Initial program 75.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 75.0%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 75.0%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 78.1%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 78.1%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 100.0%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d4 around 0 87.7%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 87.7%

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

      2. associate--r+ 87.7%

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

   6. Simplified 87.7%

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

   7. Taylor expanded in d1 around inf 72.7%

      \[\leadsto d1 \cdot \color{blue}{\left(-1 \cdot d1\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 72.7%

         \[\leadsto d1 \cdot \color{blue}{\left(-d1\right)} \]

   9. Simplified 72.7%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq -5.9 \cdot 10^{+141}:\\ \;\;\;\;d1 \cdot \left(-d3\right)\\ \mathbf{elif}\;d3 \leq -9 \cdot 10^{+65}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{elif}\;d3 \leq -3.2 \cdot 10^{-47}:\\ \;\;\;\;d1 \cdot \left(-d1\right)\\ \mathbf{elif}\;d3 \leq 1.1 \cdot 10^{+38}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{elif}\;d3 \leq 7 \cdot 10^{+110}:\\ \;\;\;\;d1 \cdot \left(-d1\right)\\ \mathbf{elif}\;d3 \leq 3.05 \cdot 10^{+172}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(-d3\right)\\ \end{array} \]

Alternative 3: 70.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := d1 \cdot \left(d2 + d4\right)\\ t_1 := d1 \cdot \left(d2 - d3\right)\\ t_2 := d1 \cdot \left(d2 - d1\right)\\ \mathbf{if}\;d3 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d3 \leq -3.8 \cdot 10^{+94}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d3 \leq -2.8 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d3 \leq 2.5 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;d3 \leq 8 \cdot 10^{+35}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d3 \leq 3.6 \cdot 10^{+111}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (* d1 (+ d2 d4))) (t_1 (* d1 (- d2 d3))) (t_2 (* d1 (- d2 d1))))
   (if (<= d3 -1e+144)
     t_1
     (if (<= d3 -3.8e+94)
       t_0
       (if (<= d3 -2.8e+54)
         t_1
         (if (<= d3 2.5e-28)
           t_2
           (if (<= d3 8e+35) t_0 (if (<= d3 3.6e+111) t_2 t_1))))))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * (d2 + d4);
	double t_1 = d1 * (d2 - d3);
	double t_2 = d1 * (d2 - d1);
	double tmp;
	if (d3 <= -1e+144) {
		tmp = t_1;
	} else if (d3 <= -3.8e+94) {
		tmp = t_0;
	} else if (d3 <= -2.8e+54) {
		tmp = t_1;
	} else if (d3 <= 2.5e-28) {
		tmp = t_2;
	} else if (d3 <= 8e+35) {
		tmp = t_0;
	} else if (d3 <= 3.6e+111) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = d1 * (d2 + d4)
    t_1 = d1 * (d2 - d3)
    t_2 = d1 * (d2 - d1)
    if (d3 <= (-1d+144)) then
        tmp = t_1
    else if (d3 <= (-3.8d+94)) then
        tmp = t_0
    else if (d3 <= (-2.8d+54)) then
        tmp = t_1
    else if (d3 <= 2.5d-28) then
        tmp = t_2
    else if (d3 <= 8d+35) then
        tmp = t_0
    else if (d3 <= 3.6d+111) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * (d2 + d4);
	double t_1 = d1 * (d2 - d3);
	double t_2 = d1 * (d2 - d1);
	double tmp;
	if (d3 <= -1e+144) {
		tmp = t_1;
	} else if (d3 <= -3.8e+94) {
		tmp = t_0;
	} else if (d3 <= -2.8e+54) {
		tmp = t_1;
	} else if (d3 <= 2.5e-28) {
		tmp = t_2;
	} else if (d3 <= 8e+35) {
		tmp = t_0;
	} else if (d3 <= 3.6e+111) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = d1 * (d2 + d4)
	t_1 = d1 * (d2 - d3)
	t_2 = d1 * (d2 - d1)
	tmp = 0
	if d3 <= -1e+144:
		tmp = t_1
	elif d3 <= -3.8e+94:
		tmp = t_0
	elif d3 <= -2.8e+54:
		tmp = t_1
	elif d3 <= 2.5e-28:
		tmp = t_2
	elif d3 <= 8e+35:
		tmp = t_0
	elif d3 <= 3.6e+111:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(d1 * Float64(d2 + d4))
	t_1 = Float64(d1 * Float64(d2 - d3))
	t_2 = Float64(d1 * Float64(d2 - d1))
	tmp = 0.0
	if (d3 <= -1e+144)
		tmp = t_1;
	elseif (d3 <= -3.8e+94)
		tmp = t_0;
	elseif (d3 <= -2.8e+54)
		tmp = t_1;
	elseif (d3 <= 2.5e-28)
		tmp = t_2;
	elseif (d3 <= 8e+35)
		tmp = t_0;
	elseif (d3 <= 3.6e+111)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	t_0 = d1 * (d2 + d4);
	t_1 = d1 * (d2 - d3);
	t_2 = d1 * (d2 - d1);
	tmp = 0.0;
	if (d3 <= -1e+144)
		tmp = t_1;
	elseif (d3 <= -3.8e+94)
		tmp = t_0;
	elseif (d3 <= -2.8e+54)
		tmp = t_1;
	elseif (d3 <= 2.5e-28)
		tmp = t_2;
	elseif (d3 <= 8e+35)
		tmp = t_0;
	elseif (d3 <= 3.6e+111)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := Block[{t$95$0 = N[(d1 * N[(d2 + d4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(d1 * N[(d2 - d3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(d1 * N[(d2 - d1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d3, -1e+144], t$95$1, If[LessEqual[d3, -3.8e+94], t$95$0, If[LessEqual[d3, -2.8e+54], t$95$1, If[LessEqual[d3, 2.5e-28], t$95$2, If[LessEqual[d3, 8e+35], t$95$0, If[LessEqual[d3, 3.6e+111], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if d3 < -1.00000000000000002e144 or -3.7999999999999996e94 < d3 < -2.80000000000000015e54 or 3.6000000000000002e111 < d3

   1. Initial program 83.3%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 83.3%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 83.3%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 85.7%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 89.2%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 99.9%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 99.9%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 99.9%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d4 around 0 91.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 91.0%

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

      2. associate--r+ 91.0%

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

   6. Simplified 91.0%

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

   7. Taylor expanded in d1 around 0 88.1%

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

   if -1.00000000000000002e144 < d3 < -3.7999999999999996e94 or 2.5000000000000001e-28 < d3 < 7.9999999999999997e35

   1. Initial program 80.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 80.0%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 80.0%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 83.3%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 83.3%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 100.0%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d3 around 0 90.4%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d1\right)} \]

   5. Taylor expanded in d1 around 0 80.7%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + d4\right)} \]

   if -2.80000000000000015e54 < d3 < 2.5000000000000001e-28 or 7.9999999999999997e35 < d3 < 3.6000000000000002e111

   1. Initial program 85.9%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 85.9%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 85.9%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 86.6%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 90.1%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 100.0%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d4 around 0 75.6%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 75.6%

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

      2. associate--r+ 75.6%

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

   6. Simplified 75.6%

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

   7. Taylor expanded in d3 around 0 71.9%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - d1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;d1 \cdot \left(d2 - d3\right)\\ \mathbf{elif}\;d3 \leq -3.8 \cdot 10^{+94}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{elif}\;d3 \leq -2.8 \cdot 10^{+54}:\\ \;\;\;\;d1 \cdot \left(d2 - d3\right)\\ \mathbf{elif}\;d3 \leq 2.5 \cdot 10^{-28}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{elif}\;d3 \leq 8 \cdot 10^{+35}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{elif}\;d3 \leq 3.6 \cdot 10^{+111}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d2 - d3\right)\\ \end{array} \]

Alternative 4: 67.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := d1 \cdot \left(d2 - d1\right)\\ t_1 := d1 \cdot \left(-d3\right)\\ t_2 := d1 \cdot \left(d2 + d4\right)\\ \mathbf{if}\;d3 \leq -2.9 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d3 \leq -1.45 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;d3 \leq 3.6 \cdot 10^{-28}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d3 \leq 7.4 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;d3 \leq 3.6 \cdot 10^{+132}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (* d1 (- d2 d1))) (t_1 (* d1 (- d3))) (t_2 (* d1 (+ d2 d4))))
   (if (<= d3 -2.9e+143)
     t_1
     (if (<= d3 -1.45e+74)
       t_2
       (if (<= d3 3.6e-28)
         t_0
         (if (<= d3 7.4e+37) t_2 (if (<= d3 3.6e+132) t_0 t_1)))))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * (d2 - d1);
	double t_1 = d1 * -d3;
	double t_2 = d1 * (d2 + d4);
	double tmp;
	if (d3 <= -2.9e+143) {
		tmp = t_1;
	} else if (d3 <= -1.45e+74) {
		tmp = t_2;
	} else if (d3 <= 3.6e-28) {
		tmp = t_0;
	} else if (d3 <= 7.4e+37) {
		tmp = t_2;
	} else if (d3 <= 3.6e+132) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = d1 * (d2 - d1)
    t_1 = d1 * -d3
    t_2 = d1 * (d2 + d4)
    if (d3 <= (-2.9d+143)) then
        tmp = t_1
    else if (d3 <= (-1.45d+74)) then
        tmp = t_2
    else if (d3 <= 3.6d-28) then
        tmp = t_0
    else if (d3 <= 7.4d+37) then
        tmp = t_2
    else if (d3 <= 3.6d+132) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * (d2 - d1);
	double t_1 = d1 * -d3;
	double t_2 = d1 * (d2 + d4);
	double tmp;
	if (d3 <= -2.9e+143) {
		tmp = t_1;
	} else if (d3 <= -1.45e+74) {
		tmp = t_2;
	} else if (d3 <= 3.6e-28) {
		tmp = t_0;
	} else if (d3 <= 7.4e+37) {
		tmp = t_2;
	} else if (d3 <= 3.6e+132) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = d1 * (d2 - d1)
	t_1 = d1 * -d3
	t_2 = d1 * (d2 + d4)
	tmp = 0
	if d3 <= -2.9e+143:
		tmp = t_1
	elif d3 <= -1.45e+74:
		tmp = t_2
	elif d3 <= 3.6e-28:
		tmp = t_0
	elif d3 <= 7.4e+37:
		tmp = t_2
	elif d3 <= 3.6e+132:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(d1 * Float64(d2 - d1))
	t_1 = Float64(d1 * Float64(-d3))
	t_2 = Float64(d1 * Float64(d2 + d4))
	tmp = 0.0
	if (d3 <= -2.9e+143)
		tmp = t_1;
	elseif (d3 <= -1.45e+74)
		tmp = t_2;
	elseif (d3 <= 3.6e-28)
		tmp = t_0;
	elseif (d3 <= 7.4e+37)
		tmp = t_2;
	elseif (d3 <= 3.6e+132)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	t_0 = d1 * (d2 - d1);
	t_1 = d1 * -d3;
	t_2 = d1 * (d2 + d4);
	tmp = 0.0;
	if (d3 <= -2.9e+143)
		tmp = t_1;
	elseif (d3 <= -1.45e+74)
		tmp = t_2;
	elseif (d3 <= 3.6e-28)
		tmp = t_0;
	elseif (d3 <= 7.4e+37)
		tmp = t_2;
	elseif (d3 <= 3.6e+132)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := Block[{t$95$0 = N[(d1 * N[(d2 - d1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(d1 * (-d3)), $MachinePrecision]}, Block[{t$95$2 = N[(d1 * N[(d2 + d4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d3, -2.9e+143], t$95$1, If[LessEqual[d3, -1.45e+74], t$95$2, If[LessEqual[d3, 3.6e-28], t$95$0, If[LessEqual[d3, 7.4e+37], t$95$2, If[LessEqual[d3, 3.6e+132], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if d3 < -2.8999999999999998e143 or 3.60000000000000016e132 < d3

   1. Initial program 84.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 84.0%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 84.0%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 86.6%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 90.6%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 99.9%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 99.9%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 99.9%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d3 around inf 76.9%

      \[\leadsto \color{blue}{-1 \cdot \left(d1 \cdot d3\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 76.9%

         \[\leadsto \color{blue}{\left(-1 \cdot d1\right) \cdot d3} \]

      2. neg-mul-1 76.9%

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

   6. Simplified 76.9%

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

   if -2.8999999999999998e143 < d3 < -1.4500000000000001e74 or 3.5999999999999999e-28 < d3 < 7.3999999999999999e37

   1. Initial program 82.4%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 82.4%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 82.4%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 85.3%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 85.3%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 100.0%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d3 around 0 85.8%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d1\right)} \]

   5. Taylor expanded in d1 around 0 77.3%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 + d4\right)} \]

   if -1.4500000000000001e74 < d3 < 3.5999999999999999e-28 or 7.3999999999999999e37 < d3 < 3.60000000000000016e132

   1. Initial program 85.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 85.0%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 85.0%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 85.7%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 89.1%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 100.0%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d4 around 0 75.1%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 75.1%

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

      2. associate--r+ 75.1%

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

   6. Simplified 75.1%

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

   7. Taylor expanded in d3 around 0 70.9%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - d1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq -2.9 \cdot 10^{+143}:\\ \;\;\;\;d1 \cdot \left(-d3\right)\\ \mathbf{elif}\;d3 \leq -1.45 \cdot 10^{+74}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{elif}\;d3 \leq 3.6 \cdot 10^{-28}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{elif}\;d3 \leq 7.4 \cdot 10^{+37}:\\ \;\;\;\;d1 \cdot \left(d2 + d4\right)\\ \mathbf{elif}\;d3 \leq 3.6 \cdot 10^{+132}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(-d3\right)\\ \end{array} \]

Alternative 5: 69.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := d1 \cdot \left(d2 - d3\right)\\ t_1 := d1 \cdot \left(d4 - d1\right)\\ \mathbf{if}\;d3 \leq -8.5 \cdot 10^{+107}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d3 \leq -2.5 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d3 \leq -4.5 \cdot 10^{+54}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d3 \leq 1.22 \cdot 10^{-107}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{elif}\;d3 \leq 5.6 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (* d1 (- d2 d3))) (t_1 (* d1 (- d4 d1))))
   (if (<= d3 -8.5e+107)
     t_0
     (if (<= d3 -2.5e+95)
       t_1
       (if (<= d3 -4.5e+54)
         t_0
         (if (<= d3 1.22e-107)
           (* d1 (- d2 d1))
           (if (<= d3 5.6e+172) t_1 t_0)))))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * (d2 - d3);
	double t_1 = d1 * (d4 - d1);
	double tmp;
	if (d3 <= -8.5e+107) {
		tmp = t_0;
	} else if (d3 <= -2.5e+95) {
		tmp = t_1;
	} else if (d3 <= -4.5e+54) {
		tmp = t_0;
	} else if (d3 <= 1.22e-107) {
		tmp = d1 * (d2 - d1);
	} else if (d3 <= 5.6e+172) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = d1 * (d2 - d3)
    t_1 = d1 * (d4 - d1)
    if (d3 <= (-8.5d+107)) then
        tmp = t_0
    else if (d3 <= (-2.5d+95)) then
        tmp = t_1
    else if (d3 <= (-4.5d+54)) then
        tmp = t_0
    else if (d3 <= 1.22d-107) then
        tmp = d1 * (d2 - d1)
    else if (d3 <= 5.6d+172) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * (d2 - d3);
	double t_1 = d1 * (d4 - d1);
	double tmp;
	if (d3 <= -8.5e+107) {
		tmp = t_0;
	} else if (d3 <= -2.5e+95) {
		tmp = t_1;
	} else if (d3 <= -4.5e+54) {
		tmp = t_0;
	} else if (d3 <= 1.22e-107) {
		tmp = d1 * (d2 - d1);
	} else if (d3 <= 5.6e+172) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = d1 * (d2 - d3)
	t_1 = d1 * (d4 - d1)
	tmp = 0
	if d3 <= -8.5e+107:
		tmp = t_0
	elif d3 <= -2.5e+95:
		tmp = t_1
	elif d3 <= -4.5e+54:
		tmp = t_0
	elif d3 <= 1.22e-107:
		tmp = d1 * (d2 - d1)
	elif d3 <= 5.6e+172:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(d1 * Float64(d2 - d3))
	t_1 = Float64(d1 * Float64(d4 - d1))
	tmp = 0.0
	if (d3 <= -8.5e+107)
		tmp = t_0;
	elseif (d3 <= -2.5e+95)
		tmp = t_1;
	elseif (d3 <= -4.5e+54)
		tmp = t_0;
	elseif (d3 <= 1.22e-107)
		tmp = Float64(d1 * Float64(d2 - d1));
	elseif (d3 <= 5.6e+172)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	t_0 = d1 * (d2 - d3);
	t_1 = d1 * (d4 - d1);
	tmp = 0.0;
	if (d3 <= -8.5e+107)
		tmp = t_0;
	elseif (d3 <= -2.5e+95)
		tmp = t_1;
	elseif (d3 <= -4.5e+54)
		tmp = t_0;
	elseif (d3 <= 1.22e-107)
		tmp = d1 * (d2 - d1);
	elseif (d3 <= 5.6e+172)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := Block[{t$95$0 = N[(d1 * N[(d2 - d3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(d1 * N[(d4 - d1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d3, -8.5e+107], t$95$0, If[LessEqual[d3, -2.5e+95], t$95$1, If[LessEqual[d3, -4.5e+54], t$95$0, If[LessEqual[d3, 1.22e-107], N[(d1 * N[(d2 - d1), $MachinePrecision]), $MachinePrecision], If[LessEqual[d3, 5.6e+172], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if d3 < -8.4999999999999999e107 or -2.50000000000000012e95 < d3 < -4.49999999999999984e54 or 5.5999999999999999e172 < d3

   1. Initial program 81.2%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 81.2%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 81.2%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 85.0%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 88.7%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 99.9%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 99.9%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 99.9%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d4 around 0 89.4%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 89.4%

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

      2. associate--r+ 89.4%

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

   6. Simplified 89.4%

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

   7. Taylor expanded in d1 around 0 85.1%

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

   if -8.4999999999999999e107 < d3 < -2.50000000000000012e95 or 1.22000000000000001e-107 < d3 < 5.5999999999999999e172

   1. Initial program 84.1%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 84.1%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 84.1%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 85.7%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 85.7%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 100.0%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d2 around 0 76.1%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--r+ 76.1%

         \[\leadsto d1 \cdot \color{blue}{\left(\left(d4 - d1\right) - d3\right)} \]

   6. Simplified 76.1%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 - d1\right) - d3\right)} \]

   7. Taylor expanded in d3 around 0 60.4%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - d1\right)} \]

   if -4.49999999999999984e54 < d3 < 1.22000000000000001e-107

   1. Initial program 86.7%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 86.7%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 86.7%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 86.7%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 91.1%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 100.0%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d4 around 0 74.5%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 74.5%

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

      2. associate--r+ 74.5%

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

   6. Simplified 74.5%

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

   7. Taylor expanded in d3 around 0 73.1%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - d1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq -8.5 \cdot 10^{+107}:\\ \;\;\;\;d1 \cdot \left(d2 - d3\right)\\ \mathbf{elif}\;d3 \leq -2.5 \cdot 10^{+95}:\\ \;\;\;\;d1 \cdot \left(d4 - d1\right)\\ \mathbf{elif}\;d3 \leq -4.5 \cdot 10^{+54}:\\ \;\;\;\;d1 \cdot \left(d2 - d3\right)\\ \mathbf{elif}\;d3 \leq 1.22 \cdot 10^{-107}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{elif}\;d3 \leq 5.6 \cdot 10^{+172}:\\ \;\;\;\;d1 \cdot \left(d4 - d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d2 - d3\right)\\ \end{array} \]

Alternative 6: 39.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := d1 \cdot \left(-d1\right)\\ t_1 := d1 \cdot \left(-d3\right)\\ \mathbf{if}\;d2 \leq -2.95 \cdot 10^{+46}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d2 \leq -6.2 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d2 \leq -4 \cdot 10^{-243}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d2 \leq -8.5 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d2 \leq 1.25 \cdot 10^{-168}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d4\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (* d1 (- d1))) (t_1 (* d1 (- d3))))
   (if (<= d2 -2.95e+46)
     (* d1 d2)
     (if (<= d2 -6.2e-52)
       t_1
       (if (<= d2 -4e-243)
         t_0
         (if (<= d2 -8.5e-279) t_1 (if (<= d2 1.25e-168) t_0 (* d1 d4))))))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * -d1;
	double t_1 = d1 * -d3;
	double tmp;
	if (d2 <= -2.95e+46) {
		tmp = d1 * d2;
	} else if (d2 <= -6.2e-52) {
		tmp = t_1;
	} else if (d2 <= -4e-243) {
		tmp = t_0;
	} else if (d2 <= -8.5e-279) {
		tmp = t_1;
	} else if (d2 <= 1.25e-168) {
		tmp = t_0;
	} else {
		tmp = d1 * d4;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = d1 * -d1
    t_1 = d1 * -d3
    if (d2 <= (-2.95d+46)) then
        tmp = d1 * d2
    else if (d2 <= (-6.2d-52)) then
        tmp = t_1
    else if (d2 <= (-4d-243)) then
        tmp = t_0
    else if (d2 <= (-8.5d-279)) then
        tmp = t_1
    else if (d2 <= 1.25d-168) then
        tmp = t_0
    else
        tmp = d1 * d4
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * -d1;
	double t_1 = d1 * -d3;
	double tmp;
	if (d2 <= -2.95e+46) {
		tmp = d1 * d2;
	} else if (d2 <= -6.2e-52) {
		tmp = t_1;
	} else if (d2 <= -4e-243) {
		tmp = t_0;
	} else if (d2 <= -8.5e-279) {
		tmp = t_1;
	} else if (d2 <= 1.25e-168) {
		tmp = t_0;
	} else {
		tmp = d1 * d4;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = d1 * -d1
	t_1 = d1 * -d3
	tmp = 0
	if d2 <= -2.95e+46:
		tmp = d1 * d2
	elif d2 <= -6.2e-52:
		tmp = t_1
	elif d2 <= -4e-243:
		tmp = t_0
	elif d2 <= -8.5e-279:
		tmp = t_1
	elif d2 <= 1.25e-168:
		tmp = t_0
	else:
		tmp = d1 * d4
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(d1 * Float64(-d1))
	t_1 = Float64(d1 * Float64(-d3))
	tmp = 0.0
	if (d2 <= -2.95e+46)
		tmp = Float64(d1 * d2);
	elseif (d2 <= -6.2e-52)
		tmp = t_1;
	elseif (d2 <= -4e-243)
		tmp = t_0;
	elseif (d2 <= -8.5e-279)
		tmp = t_1;
	elseif (d2 <= 1.25e-168)
		tmp = t_0;
	else
		tmp = Float64(d1 * d4);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	t_0 = d1 * -d1;
	t_1 = d1 * -d3;
	tmp = 0.0;
	if (d2 <= -2.95e+46)
		tmp = d1 * d2;
	elseif (d2 <= -6.2e-52)
		tmp = t_1;
	elseif (d2 <= -4e-243)
		tmp = t_0;
	elseif (d2 <= -8.5e-279)
		tmp = t_1;
	elseif (d2 <= 1.25e-168)
		tmp = t_0;
	else
		tmp = d1 * d4;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := Block[{t$95$0 = N[(d1 * (-d1)), $MachinePrecision]}, Block[{t$95$1 = N[(d1 * (-d3)), $MachinePrecision]}, If[LessEqual[d2, -2.95e+46], N[(d1 * d2), $MachinePrecision], If[LessEqual[d2, -6.2e-52], t$95$1, If[LessEqual[d2, -4e-243], t$95$0, If[LessEqual[d2, -8.5e-279], t$95$1, If[LessEqual[d2, 1.25e-168], t$95$0, N[(d1 * d4), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if d2 < -2.95e46

   1. Initial program 75.4%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 75.4%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 75.4%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 79.2%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 84.8%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 99.9%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 99.9%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 99.9%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d2 around inf 64.3%

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

   if -2.95e46 < d2 < -6.1999999999999998e-52 or -3.99999999999999998e-243 < d2 < -8.5000000000000002e-279

   1. Initial program 83.3%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 83.3%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 83.3%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 83.3%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 83.3%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 100.0%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d3 around inf 35.0%

      \[\leadsto \color{blue}{-1 \cdot \left(d1 \cdot d3\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 35.0%

         \[\leadsto \color{blue}{\left(-1 \cdot d1\right) \cdot d3} \]

      2. neg-mul-1 35.0%

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

   6. Simplified 35.0%

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

   if -6.1999999999999998e-52 < d2 < -3.99999999999999998e-243 or -8.5000000000000002e-279 < d2 < 1.25e-168

   1. Initial program 96.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 96.0%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 96.0%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 96.0%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 96.0%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 99.9%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 99.9%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 99.9%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d4 around 0 72.5%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 72.5%

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

      2. associate--r+ 72.5%

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

   6. Simplified 72.5%

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

   7. Taylor expanded in d1 around inf 42.4%

      \[\leadsto d1 \cdot \color{blue}{\left(-1 \cdot d1\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 42.4%

         \[\leadsto d1 \cdot \color{blue}{\left(-d1\right)} \]

   9. Simplified 42.4%

      \[\leadsto d1 \cdot \color{blue}{\left(-d1\right)} \]

   if 1.25e-168 < d2

   1. Initial program 80.7%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 80.7%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 80.7%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 82.6%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 87.1%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 100.0%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d4 around inf 25.4%

      \[\leadsto \color{blue}{d1 \cdot d4} \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -2.95 \cdot 10^{+46}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d2 \leq -6.2 \cdot 10^{-52}:\\ \;\;\;\;d1 \cdot \left(-d3\right)\\ \mathbf{elif}\;d2 \leq -4 \cdot 10^{-243}:\\ \;\;\;\;d1 \cdot \left(-d1\right)\\ \mathbf{elif}\;d2 \leq -8.5 \cdot 10^{-279}:\\ \;\;\;\;d1 \cdot \left(-d3\right)\\ \mathbf{elif}\;d2 \leq 1.25 \cdot 10^{-168}:\\ \;\;\;\;d1 \cdot \left(-d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d4\\ \end{array} \]

Alternative 7: 61.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := d1 \cdot \left(d2 - d1\right)\\ \mathbf{if}\;d4 \leq -2.8 \cdot 10^{-207}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d4 \leq 1.5 \cdot 10^{-280}:\\ \;\;\;\;d1 \cdot \left(d2 - d3\right)\\ \mathbf{elif}\;d4 \leq 4.8 \cdot 10^{-30}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (let* ((t_0 (* d1 (- d2 d1))))
   (if (<= d4 -2.8e-207)
     t_0
     (if (<= d4 1.5e-280)
       (* d1 (- d2 d3))
       (if (<= d4 4.8e-30) t_0 (* d1 (- d4 d3)))))))

C

double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * (d2 - d1);
	double tmp;
	if (d4 <= -2.8e-207) {
		tmp = t_0;
	} else if (d4 <= 1.5e-280) {
		tmp = d1 * (d2 - d3);
	} else if (d4 <= 4.8e-30) {
		tmp = t_0;
	} else {
		tmp = d1 * (d4 - d3);
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: t_0
    real(8) :: tmp
    t_0 = d1 * (d2 - d1)
    if (d4 <= (-2.8d-207)) then
        tmp = t_0
    else if (d4 <= 1.5d-280) then
        tmp = d1 * (d2 - d3)
    else if (d4 <= 4.8d-30) then
        tmp = t_0
    else
        tmp = d1 * (d4 - d3)
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double t_0 = d1 * (d2 - d1);
	double tmp;
	if (d4 <= -2.8e-207) {
		tmp = t_0;
	} else if (d4 <= 1.5e-280) {
		tmp = d1 * (d2 - d3);
	} else if (d4 <= 4.8e-30) {
		tmp = t_0;
	} else {
		tmp = d1 * (d4 - d3);
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	t_0 = d1 * (d2 - d1)
	tmp = 0
	if d4 <= -2.8e-207:
		tmp = t_0
	elif d4 <= 1.5e-280:
		tmp = d1 * (d2 - d3)
	elif d4 <= 4.8e-30:
		tmp = t_0
	else:
		tmp = d1 * (d4 - d3)
	return tmp

Julia

function code(d1, d2, d3, d4)
	t_0 = Float64(d1 * Float64(d2 - d1))
	tmp = 0.0
	if (d4 <= -2.8e-207)
		tmp = t_0;
	elseif (d4 <= 1.5e-280)
		tmp = Float64(d1 * Float64(d2 - d3));
	elseif (d4 <= 4.8e-30)
		tmp = t_0;
	else
		tmp = Float64(d1 * Float64(d4 - d3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	t_0 = d1 * (d2 - d1);
	tmp = 0.0;
	if (d4 <= -2.8e-207)
		tmp = t_0;
	elseif (d4 <= 1.5e-280)
		tmp = d1 * (d2 - d3);
	elseif (d4 <= 4.8e-30)
		tmp = t_0;
	else
		tmp = d1 * (d4 - d3);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := Block[{t$95$0 = N[(d1 * N[(d2 - d1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d4, -2.8e-207], t$95$0, If[LessEqual[d4, 1.5e-280], N[(d1 * N[(d2 - d3), $MachinePrecision]), $MachinePrecision], If[LessEqual[d4, 4.8e-30], t$95$0, N[(d1 * N[(d4 - d3), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if d4 < -2.79999999999999993e-207 or 1.49999999999999994e-280 < d4 < 4.7999999999999997e-30

   1. Initial program 84.9%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 84.9%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 84.9%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 87.4%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 89.3%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 100.0%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d4 around 0 82.4%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 82.4%

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

      2. associate--r+ 82.4%

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

   6. Simplified 82.4%

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

   7. Taylor expanded in d3 around 0 61.1%

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

   if -2.79999999999999993e-207 < d4 < 1.49999999999999994e-280

   1. Initial program 92.6%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 92.6%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 92.6%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 92.6%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 92.6%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 99.9%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 99.9%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 99.9%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d4 around 0 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 99.9%

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

      2. associate--r+ 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in d1 around 0 59.6%

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

   if 4.7999999999999997e-30 < d4

   1. Initial program 80.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 80.0%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 80.0%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 80.0%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 87.1%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 99.9%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 99.9%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 99.9%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d2 around 0 88.4%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--r+ 88.4%

         \[\leadsto d1 \cdot \color{blue}{\left(\left(d4 - d1\right) - d3\right)} \]

   6. Simplified 88.4%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 - d1\right) - d3\right)} \]

   7. Taylor expanded in d1 around 0 73.7%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - d3\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d4 \leq -2.8 \cdot 10^{-207}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{elif}\;d4 \leq 1.5 \cdot 10^{-280}:\\ \;\;\;\;d1 \cdot \left(d2 - d3\right)\\ \mathbf{elif}\;d4 \leq 4.8 \cdot 10^{-30}:\\ \;\;\;\;d1 \cdot \left(d2 - d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d3\right)\\ \end{array} \]

Alternative 8: 88.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d3 \leq -2.8 \cdot 10^{+143}:\\ \;\;\;\;d1 \cdot \left(d2 - d3\right)\\ \mathbf{elif}\;d3 \leq 2.5 \cdot 10^{+111}:\\ \;\;\;\;d1 \cdot \left(\left(d2 + d4\right) - d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d3 -2.8e+143)
   (* d1 (- d2 d3))
   (if (<= d3 2.5e+111) (* d1 (- (+ d2 d4) d1)) (* d1 (- d4 d3)))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d3 <= -2.8e+143) {
		tmp = d1 * (d2 - d3);
	} else if (d3 <= 2.5e+111) {
		tmp = d1 * ((d2 + d4) - d1);
	} else {
		tmp = d1 * (d4 - d3);
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d3 <= (-2.8d+143)) then
        tmp = d1 * (d2 - d3)
    else if (d3 <= 2.5d+111) then
        tmp = d1 * ((d2 + d4) - d1)
    else
        tmp = d1 * (d4 - d3)
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d3 <= -2.8e+143) {
		tmp = d1 * (d2 - d3);
	} else if (d3 <= 2.5e+111) {
		tmp = d1 * ((d2 + d4) - d1);
	} else {
		tmp = d1 * (d4 - d3);
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d3 <= -2.8e+143:
		tmp = d1 * (d2 - d3)
	elif d3 <= 2.5e+111:
		tmp = d1 * ((d2 + d4) - d1)
	else:
		tmp = d1 * (d4 - d3)
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d3 <= -2.8e+143)
		tmp = Float64(d1 * Float64(d2 - d3));
	elseif (d3 <= 2.5e+111)
		tmp = Float64(d1 * Float64(Float64(d2 + d4) - d1));
	else
		tmp = Float64(d1 * Float64(d4 - d3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d3 <= -2.8e+143)
		tmp = d1 * (d2 - d3);
	elseif (d3 <= 2.5e+111)
		tmp = d1 * ((d2 + d4) - d1);
	else
		tmp = d1 * (d4 - d3);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d3, -2.8e+143], N[(d1 * N[(d2 - d3), $MachinePrecision]), $MachinePrecision], If[LessEqual[d3, 2.5e+111], N[(d1 * N[(N[(d2 + d4), $MachinePrecision] - d1), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d4 - d3), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d3 < -2.79999999999999998e143

   1. Initial program 83.8%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 83.8%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 83.8%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 87.0%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 87.0%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 99.9%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 99.9%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 99.9%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d4 around 0 96.9%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 96.9%

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

      2. associate--r+ 96.9%

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

   6. Simplified 96.9%

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

   7. Taylor expanded in d1 around 0 89.2%

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

   if -2.79999999999999998e143 < d3 < 2.4999999999999998e111

   1. Initial program 85.4%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 85.4%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 85.4%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 86.5%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 89.3%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 100.0%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d3 around 0 93.3%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d1\right)} \]

   if 2.4999999999999998e111 < d3

   1. Initial program 80.9%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 80.9%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 80.9%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 83.0%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 89.3%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 99.9%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 99.9%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 99.9%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d2 around 0 86.5%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--r+ 86.5%

         \[\leadsto d1 \cdot \color{blue}{\left(\left(d4 - d1\right) - d3\right)} \]

   6. Simplified 86.5%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 - d1\right) - d3\right)} \]

   7. Taylor expanded in d1 around 0 84.3%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - d3\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq -2.8 \cdot 10^{+143}:\\ \;\;\;\;d1 \cdot \left(d2 - d3\right)\\ \mathbf{elif}\;d3 \leq 2.5 \cdot 10^{+111}:\\ \;\;\;\;d1 \cdot \left(\left(d2 + d4\right) - d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d3\right)\\ \end{array} \]

Alternative 9: 90.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d3 \leq -4.7 \cdot 10^{+141}:\\ \;\;\;\;d1 \cdot \left(\left(d2 - d3\right) - d1\right)\\ \mathbf{elif}\;d3 \leq 2.35 \cdot 10^{+113}:\\ \;\;\;\;d1 \cdot \left(\left(d2 + d4\right) - d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d3 -4.7e+141)
   (* d1 (- (- d2 d3) d1))
   (if (<= d3 2.35e+113) (* d1 (- (+ d2 d4) d1)) (* d1 (- d4 d3)))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d3 <= -4.7e+141) {
		tmp = d1 * ((d2 - d3) - d1);
	} else if (d3 <= 2.35e+113) {
		tmp = d1 * ((d2 + d4) - d1);
	} else {
		tmp = d1 * (d4 - d3);
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d3 <= (-4.7d+141)) then
        tmp = d1 * ((d2 - d3) - d1)
    else if (d3 <= 2.35d+113) then
        tmp = d1 * ((d2 + d4) - d1)
    else
        tmp = d1 * (d4 - d3)
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d3 <= -4.7e+141) {
		tmp = d1 * ((d2 - d3) - d1);
	} else if (d3 <= 2.35e+113) {
		tmp = d1 * ((d2 + d4) - d1);
	} else {
		tmp = d1 * (d4 - d3);
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d3 <= -4.7e+141:
		tmp = d1 * ((d2 - d3) - d1)
	elif d3 <= 2.35e+113:
		tmp = d1 * ((d2 + d4) - d1)
	else:
		tmp = d1 * (d4 - d3)
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d3 <= -4.7e+141)
		tmp = Float64(d1 * Float64(Float64(d2 - d3) - d1));
	elseif (d3 <= 2.35e+113)
		tmp = Float64(d1 * Float64(Float64(d2 + d4) - d1));
	else
		tmp = Float64(d1 * Float64(d4 - d3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d3 <= -4.7e+141)
		tmp = d1 * ((d2 - d3) - d1);
	elseif (d3 <= 2.35e+113)
		tmp = d1 * ((d2 + d4) - d1);
	else
		tmp = d1 * (d4 - d3);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d3, -4.7e+141], N[(d1 * N[(N[(d2 - d3), $MachinePrecision] - d1), $MachinePrecision]), $MachinePrecision], If[LessEqual[d3, 2.35e+113], N[(d1 * N[(N[(d2 + d4), $MachinePrecision] - d1), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d4 - d3), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d3 < -4.69999999999999979e141

   1. Initial program 83.8%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 83.8%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 83.8%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 87.0%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 87.0%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 99.9%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 99.9%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 99.9%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d4 around 0 96.9%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 96.9%

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

      2. associate--r+ 96.9%

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

   6. Simplified 96.9%

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

   if -4.69999999999999979e141 < d3 < 2.3499999999999999e113

   1. Initial program 85.4%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 85.4%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 85.4%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 86.5%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 89.3%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 100.0%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d3 around 0 93.3%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d1\right)} \]

   if 2.3499999999999999e113 < d3

   1. Initial program 80.9%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 80.9%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 80.9%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 83.0%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 89.3%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 99.9%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 99.9%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 99.9%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d2 around 0 86.5%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--r+ 86.5%

         \[\leadsto d1 \cdot \color{blue}{\left(\left(d4 - d1\right) - d3\right)} \]

   6. Simplified 86.5%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 - d1\right) - d3\right)} \]

   7. Taylor expanded in d1 around 0 84.3%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - d3\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq -4.7 \cdot 10^{+141}:\\ \;\;\;\;d1 \cdot \left(\left(d2 - d3\right) - d1\right)\\ \mathbf{elif}\;d3 \leq 2.35 \cdot 10^{+113}:\\ \;\;\;\;d1 \cdot \left(\left(d2 + d4\right) - d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d3\right)\\ \end{array} \]

Alternative 10: 62.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -1.7 \cdot 10^{-17}:\\ \;\;\;\;d1 \cdot \left(d2 - d3\right)\\ \mathbf{elif}\;d2 \leq 3.5 \cdot 10^{-173}:\\ \;\;\;\;d1 \cdot \left(\left(-d3\right) - d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -1.7e-17)
   (* d1 (- d2 d3))
   (if (<= d2 3.5e-173) (* d1 (- (- d3) d1)) (* d1 (- d4 d3)))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -1.7e-17) {
		tmp = d1 * (d2 - d3);
	} else if (d2 <= 3.5e-173) {
		tmp = d1 * (-d3 - d1);
	} else {
		tmp = d1 * (d4 - d3);
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d2 <= (-1.7d-17)) then
        tmp = d1 * (d2 - d3)
    else if (d2 <= 3.5d-173) then
        tmp = d1 * (-d3 - d1)
    else
        tmp = d1 * (d4 - d3)
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -1.7e-17) {
		tmp = d1 * (d2 - d3);
	} else if (d2 <= 3.5e-173) {
		tmp = d1 * (-d3 - d1);
	} else {
		tmp = d1 * (d4 - d3);
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -1.7e-17:
		tmp = d1 * (d2 - d3)
	elif d2 <= 3.5e-173:
		tmp = d1 * (-d3 - d1)
	else:
		tmp = d1 * (d4 - d3)
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d2 <= -1.7e-17)
		tmp = Float64(d1 * Float64(d2 - d3));
	elseif (d2 <= 3.5e-173)
		tmp = Float64(d1 * Float64(Float64(-d3) - d1));
	else
		tmp = Float64(d1 * Float64(d4 - d3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d2 <= -1.7e-17)
		tmp = d1 * (d2 - d3);
	elseif (d2 <= 3.5e-173)
		tmp = d1 * (-d3 - d1);
	else
		tmp = d1 * (d4 - d3);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d2, -1.7e-17], N[(d1 * N[(d2 - d3), $MachinePrecision]), $MachinePrecision], If[LessEqual[d2, 3.5e-173], N[(d1 * N[((-d3) - d1), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(d4 - d3), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d2 < -1.6999999999999999e-17

   1. Initial program 76.2%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 76.2%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 76.2%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 79.6%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 84.7%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 99.9%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 99.9%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 99.9%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d4 around 0 88.1%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 88.1%

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

      2. associate--r+ 88.1%

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

   6. Simplified 88.1%

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

   7. Taylor expanded in d1 around 0 73.8%

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

   if -1.6999999999999999e-17 < d2 < 3.50000000000000014e-173

   1. Initial program 94.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 94.0%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 94.0%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 94.0%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 94.0%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 99.9%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 99.9%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 99.9%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d4 around 0 70.5%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 70.5%

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

      2. associate--r+ 70.5%

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

   6. Simplified 70.5%

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

   7. Taylor expanded in d2 around 0 68.3%

      \[\leadsto \color{blue}{-1 \cdot \left(d1 \cdot \left(d1 + d3\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 68.3%

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

      2. distribute-rgt-neg-in 68.3%

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

      3. distribute-neg-in 68.3%

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

      4. +-commutative 68.3%

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

      5. sub-neg 68.3%

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

   9. Simplified 68.3%

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

   if 3.50000000000000014e-173 < d2

   1. Initial program 81.4%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 81.4%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 81.4%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 83.2%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 87.6%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 100.0%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d2 around 0 77.3%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--r+ 77.3%

         \[\leadsto d1 \cdot \color{blue}{\left(\left(d4 - d1\right) - d3\right)} \]

   6. Simplified 77.3%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 - d1\right) - d3\right)} \]

   7. Taylor expanded in d1 around 0 51.7%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - d3\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -1.7 \cdot 10^{-17}:\\ \;\;\;\;d1 \cdot \left(d2 - d3\right)\\ \mathbf{elif}\;d2 \leq 3.5 \cdot 10^{-173}:\\ \;\;\;\;d1 \cdot \left(\left(-d3\right) - d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(d4 - d3\right)\\ \end{array} \]

Alternative 11: 83.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 6.4 \cdot 10^{-35}:\\ \;\;\;\;d1 \cdot \left(\left(d2 - d3\right) - d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(\left(d4 - d1\right) - d3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 6.4e-35) (* d1 (- (- d2 d3) d1)) (* d1 (- (- d4 d1) d3))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 6.4e-35) {
		tmp = d1 * ((d2 - d3) - d1);
	} else {
		tmp = d1 * ((d4 - d1) - d3);
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d4 <= 6.4d-35) then
        tmp = d1 * ((d2 - d3) - d1)
    else
        tmp = d1 * ((d4 - d1) - d3)
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 6.4e-35) {
		tmp = d1 * ((d2 - d3) - d1);
	} else {
		tmp = d1 * ((d4 - d1) - d3);
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 6.4e-35:
		tmp = d1 * ((d2 - d3) - d1)
	else:
		tmp = d1 * ((d4 - d1) - d3)
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 6.4e-35)
		tmp = Float64(d1 * Float64(Float64(d2 - d3) - d1));
	else
		tmp = Float64(d1 * Float64(Float64(d4 - d1) - d3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d4 <= 6.4e-35)
		tmp = d1 * ((d2 - d3) - d1);
	else
		tmp = d1 * ((d4 - d1) - d3);
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 6.4e-35], N[(d1 * N[(N[(d2 - d3), $MachinePrecision] - d1), $MachinePrecision]), $MachinePrecision], N[(d1 * N[(N[(d4 - d1), $MachinePrecision] - d3), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d4 < 6.3999999999999996e-35

   1. Initial program 86.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 86.0%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 86.0%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 88.1%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 89.8%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 100.0%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d4 around 0 84.9%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 84.9%

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

      2. associate--r+ 84.9%

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

   6. Simplified 84.9%

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

   if 6.3999999999999996e-35 < d4

   1. Initial program 80.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 80.0%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 80.0%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 80.0%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 87.1%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 99.9%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 99.9%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 99.9%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d2 around 0 88.4%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - \left(d1 + d3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--r+ 88.4%

         \[\leadsto d1 \cdot \color{blue}{\left(\left(d4 - d1\right) - d3\right)} \]

   6. Simplified 88.4%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 - d1\right) - d3\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d4 \leq 6.4 \cdot 10^{-35}:\\ \;\;\;\;d1 \cdot \left(\left(d2 - d3\right) - d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot \left(\left(d4 - d1\right) - d3\right)\\ \end{array} \]

Alternative 12: 38.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -1.7 \cdot 10^{-17}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d2 \leq 5.6 \cdot 10^{-167}:\\ \;\;\;\;d1 \cdot \left(-d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d4\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -1.7e-17) (* d1 d2) (if (<= d2 5.6e-167) (* d1 (- d1)) (* d1 d4))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -1.7e-17) {
		tmp = d1 * d2;
	} else if (d2 <= 5.6e-167) {
		tmp = d1 * -d1;
	} else {
		tmp = d1 * d4;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d2 <= (-1.7d-17)) then
        tmp = d1 * d2
    else if (d2 <= 5.6d-167) then
        tmp = d1 * -d1
    else
        tmp = d1 * d4
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -1.7e-17) {
		tmp = d1 * d2;
	} else if (d2 <= 5.6e-167) {
		tmp = d1 * -d1;
	} else {
		tmp = d1 * d4;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -1.7e-17:
		tmp = d1 * d2
	elif d2 <= 5.6e-167:
		tmp = d1 * -d1
	else:
		tmp = d1 * d4
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d2 <= -1.7e-17)
		tmp = Float64(d1 * d2);
	elseif (d2 <= 5.6e-167)
		tmp = Float64(d1 * Float64(-d1));
	else
		tmp = Float64(d1 * d4);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d2 <= -1.7e-17)
		tmp = d1 * d2;
	elseif (d2 <= 5.6e-167)
		tmp = d1 * -d1;
	else
		tmp = d1 * d4;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d2, -1.7e-17], N[(d1 * d2), $MachinePrecision], If[LessEqual[d2, 5.6e-167], N[(d1 * (-d1)), $MachinePrecision], N[(d1 * d4), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d2 < -1.6999999999999999e-17

   1. Initial program 76.2%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 76.2%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 76.2%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 79.6%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 84.7%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 99.9%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 99.9%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 99.9%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d2 around inf 61.6%

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

   if -1.6999999999999999e-17 < d2 < 5.59999999999999971e-167

   1. Initial program 94.3%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 94.3%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 94.3%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 94.3%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 94.3%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 99.9%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 99.9%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 99.9%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d4 around 0 71.9%

      \[\leadsto \color{blue}{d1 \cdot \left(d2 - \left(d1 + d3\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 71.9%

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

      2. associate--r+ 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in d1 around inf 38.3%

      \[\leadsto d1 \cdot \color{blue}{\left(-1 \cdot d1\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 38.3%

         \[\leadsto d1 \cdot \color{blue}{\left(-d1\right)} \]

   9. Simplified 38.3%

      \[\leadsto d1 \cdot \color{blue}{\left(-d1\right)} \]

   if 5.59999999999999971e-167 < d2

   1. Initial program 80.7%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 80.7%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 80.7%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 82.6%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 87.1%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 100.0%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d4 around inf 25.4%

      \[\leadsto \color{blue}{d1 \cdot d4} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -1.7 \cdot 10^{-17}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{elif}\;d2 \leq 5.6 \cdot 10^{-167}:\\ \;\;\;\;d1 \cdot \left(-d1\right)\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d4\\ \end{array} \]

Alternative 13: 37.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -1.4 \cdot 10^{-33}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d4\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -1.4e-33) (* d1 d2) (* d1 d4)))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -1.4e-33) {
		tmp = d1 * d2;
	} else {
		tmp = d1 * d4;
	}
	return tmp;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d2 <= (-1.4d-33)) then
        tmp = d1 * d2
    else
        tmp = d1 * d4
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -1.4e-33) {
		tmp = d1 * d2;
	} else {
		tmp = d1 * d4;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -1.4e-33:
		tmp = d1 * d2
	else:
		tmp = d1 * d4
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d2 <= -1.4e-33)
		tmp = Float64(d1 * d2);
	else
		tmp = Float64(d1 * d4);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d2 <= -1.4e-33)
		tmp = d1 * d2;
	else
		tmp = d1 * d4;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d2, -1.4e-33], N[(d1 * d2), $MachinePrecision], N[(d1 * d4), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -1.4e-33

   1. Initial program 76.6%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 76.6%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 76.6%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 80.0%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 84.9%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 99.9%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 99.9%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 99.9%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 99.9%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 99.9%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 99.9%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 99.9%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d2 around inf 62.3%

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

   if -1.4e-33 < d2

   1. Initial program 86.7%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Step-by-step derivation

      1. +-commutative 86.7%

         \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

      2. *-commutative 86.7%

         \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

      3. distribute-lft-out-- 87.7%

         \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

      4. distribute-lft-out 90.3%

         \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

      5. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

      6. +-commutative 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

      7. associate-+l- 100.0%

         \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

      8. associate--l- 100.0%

         \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

      9. associate--r- 100.0%

         \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

      10. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

      11. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

      12. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

      13. distribute-neg-out 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

      14. remove-double-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

      15. sub-neg 100.0%

          \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

      16. +-commutative 100.0%

          \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

      17. associate--l- 100.0%

          \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

   4. Taylor expanded in d4 around inf 30.7%

      \[\leadsto \color{blue}{d1 \cdot d4} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -1.4 \cdot 10^{-33}:\\ \;\;\;\;d1 \cdot d2\\ \mathbf{else}:\\ \;\;\;\;d1 \cdot d4\\ \end{array} \]

Alternative 14: 30.7% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ d1 \cdot d2 \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4) :precision binary64 (* d1 d2))

C

double code(double d1, double d2, double d3, double d4) {
	return d1 * d2;
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    code = d1 * d2
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	return d1 * d2;
}

Python

def code(d1, d2, d3, d4):
	return d1 * d2

Julia

function code(d1, d2, d3, d4)
	return Float64(d1 * d2)
end

MATLAB

function tmp = code(d1, d2, d3, d4)
	tmp = d1 * d2;
end

Wolfram

code[d1_, d2_, d3_, d4_] := N[(d1 * d2), $MachinePrecision]

Derivation

1. Initial program 84.4%

   \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
2. Step-by-step derivation

   1. +-commutative 84.4%

      \[\leadsto \color{blue}{\left(d4 \cdot d1 + \left(d1 \cdot d2 - d1 \cdot d3\right)\right)} - d1 \cdot d1 \]

   2. *-commutative 84.4%

      \[\leadsto \left(\color{blue}{d1 \cdot d4} + \left(d1 \cdot d2 - d1 \cdot d3\right)\right) - d1 \cdot d1 \]

   3. distribute-lft-out-- 85.9%

      \[\leadsto \left(d1 \cdot d4 + \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) - d1 \cdot d1 \]

   4. distribute-lft-out 89.0%

      \[\leadsto \color{blue}{d1 \cdot \left(d4 + \left(d2 - d3\right)\right)} - d1 \cdot d1 \]

   5. distribute-lft-out-- 100.0%

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d4 + \left(d2 - d3\right)\right) - d1\right)} \]

   6. +-commutative 100.0%

      \[\leadsto d1 \cdot \left(\color{blue}{\left(\left(d2 - d3\right) + d4\right)} - d1\right) \]

   7. associate-+l- 100.0%

      \[\leadsto d1 \cdot \left(\color{blue}{\left(d2 - \left(d3 - d4\right)\right)} - d1\right) \]

   8. associate--l- 100.0%

      \[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)} \]

   9. associate--r- 100.0%

      \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 - \left(d4 - d1\right)\right)}\right) \]

   10. sub-neg 100.0%

       \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(d3 + \left(-\left(d4 - d1\right)\right)\right)}\right) \]

   11. sub-neg 100.0%

       \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(d4 + \left(-d1\right)\right)}\right)\right)\right) \]

   12. +-commutative 100.0%

       \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(-\color{blue}{\left(\left(-d1\right) + d4\right)}\right)\right)\right) \]

   13. distribute-neg-out 100.0%

       \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(\left(-\left(-d1\right)\right) + \left(-d4\right)\right)}\right)\right) \]

   14. remove-double-neg 100.0%

       \[\leadsto d1 \cdot \left(d2 - \left(d3 + \left(\color{blue}{d1} + \left(-d4\right)\right)\right)\right) \]

   15. sub-neg 100.0%

       \[\leadsto d1 \cdot \left(d2 - \left(d3 + \color{blue}{\left(d1 - d4\right)}\right)\right) \]

   16. +-commutative 100.0%

       \[\leadsto d1 \cdot \left(d2 - \color{blue}{\left(\left(d1 - d4\right) + d3\right)}\right) \]

   17. associate--l- 100.0%

       \[\leadsto d1 \cdot \color{blue}{\left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - \left(d1 - d4\right)\right) - d3\right)} \]

4. Taylor expanded in d2 around inf 31.5%

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

5. Final simplification 31.5%

   \[\leadsto d1 \cdot d2 \]

Developer target: 100.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ d1 \cdot \left(\left(\left(d2 - d3\right) + d4\right) - d1\right) \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4) :precision binary64 (* d1 (- (+ (- d2 d3) d4) d1)))

C

double code(double d1, double d2, double d3, double d4) {
	return d1 * (((d2 - d3) + d4) - d1);
}

Fortran

real(8) function code(d1, d2, d3, d4)
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    code = d1 * (((d2 - d3) + d4) - d1)
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	return d1 * (((d2 - d3) + d4) - d1);
}

Python

def code(d1, d2, d3, d4):
	return d1 * (((d2 - d3) + d4) - d1)

Julia

function code(d1, d2, d3, d4)
	return Float64(d1 * Float64(Float64(Float64(d2 - d3) + d4) - d1))
end

MATLAB

function tmp = code(d1, d2, d3, d4)
	tmp = d1 * (((d2 - d3) + d4) - d1);
end

Wolfram

code[d1_, d2_, d3_, d4_] := N[(d1 * N[(N[(N[(d2 - d3), $MachinePrecision] + d4), $MachinePrecision] - d1), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023305 
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"
  :precision binary64

  :herbie-target
  (* d1 (- (+ (- d2 d3) d4) d1))

  (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)))