Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H

Percentage Accurate: 100.0% → 100.0%

Time: 5.6s

Alternatives: 7

Speedup: 1.0×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x + y\right) \cdot \left(1 - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))

C

double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * (1.0d0 - z)
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

Python

def code(x, y, z):
	return (x + y) * (1.0 - z)

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(1.0 - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (1.0 - z);
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + y\right) \cdot \left(1 - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))

C

double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * (1.0d0 - z)
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

Python

def code(x, y, z):
	return (x + y) * (1.0 - z)

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(1.0 - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (1.0 - z);
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - z\right) \cdot \left(x + y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (- 1.0 z) (+ x y)))

C

double code(double x, double y, double z) {
	return (1.0 - z) * (x + y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (1.0d0 - z) * (x + y)
end function

Java

public static double code(double x, double y, double z) {
	return (1.0 - z) * (x + y);
}

Python

def code(x, y, z):
	return (1.0 - z) * (x + y)

Julia

function code(x, y, z)
	return Float64(Float64(1.0 - z) * Float64(x + y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (1.0 - z) * (x + y);
end

Wolfram

code[x_, y_, z_] := N[(N[(1.0 - z), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto \left(1 - z\right) \cdot \left(x + y\right) \]
4. Add Preprocessing

Alternative 2: 75.7% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := y \cdot \left(1 - z\right)\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-16}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 320000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1250000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+45} \lor \neg \left(z \leq 8 \cdot 10^{+56}\right) \land \left(z \leq 8.2 \cdot 10^{+69} \lor \neg \left(z \leq 5 \cdot 10^{+83}\right) \land \left(z \leq 6.6 \cdot 10^{+97} \lor \neg \left(z \leq 4.1 \cdot 10^{+98}\right) \land \left(z \leq 1.1 \cdot 10^{+102} \lor \neg \left(z \leq 1.5 \cdot 10^{+118}\right) \land \left(z \leq 4.2 \cdot 10^{+123} \lor \neg \left(z \leq 1.7 \cdot 10^{+127}\right) \land \left(z \leq 1.4 \cdot 10^{+142} \lor \neg \left(z \leq 1.55 \cdot 10^{+150}\right) \land \left(z \leq 5.2 \cdot 10^{+151} \lor \neg \left(z \leq 2.1 \cdot 10^{+156}\right) \land \left(z \leq 6.6 \cdot 10^{+156} \lor \neg \left(z \leq 5.4 \cdot 10^{+169}\right) \land \left(z \leq 2.3 \cdot 10^{+182} \lor \neg \left(z \leq 2.3 \cdot 10^{+185}\right) \land \left(z \leq 2.7 \cdot 10^{+191} \lor \neg \left(z \leq 8.4 \cdot 10^{+210}\right) \land \left(z \leq 9.2 \cdot 10^{+230} \lor \neg \left(z \leq 7.2 \cdot 10^{+241}\right) \land \left(z \leq 8.2 \cdot 10^{+264} \lor \neg \left(z \leq 9.5 \cdot 10^{+269}\right) \land \left(z \leq 3.5 \cdot 10^{+270} \lor \neg \left(z \leq 7.4 \cdot 10^{+282}\right) \land \left(z \leq 2.9 \cdot 10^{+283} \lor \neg \left(z \leq 9 \cdot 10^{+288}\right) \land z \leq 7.2 \cdot 10^{+291}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))) (t_1 (* y (- 1.0 z))))
   (if (<= z -2.15e-13)
     t_1
     (if (<= z 3.5e-16)
       (+ x y)
       (if (<= z 320000.0)
         t_1
         (if (<= z 1250000.0)
           t_0
           (if (<= z 3.9e+40)
             t_1
             (if (or (<= z 4.8e+45)
                     (and (not (<= z 8e+56))
                          (or (<= z 8.2e+69)
                              (and (not (<= z 5e+83))
                                   (or (<= z 6.6e+97)
                                       (and (not (<= z 4.1e+98))
                                            (or (<= z 1.1e+102)
                                                (and (not (<= z 1.5e+118))
                                                     (or (<= z 4.2e+123)
                                                         (and (not
                                                               (<= z 1.7e+127))
                                                              (or (<=
                                                                   z
                                                                   1.4e+142)
                                                                  (and (not
                                                                        (<=
                                                                         z
                                                                         1.55e+150))
                                                                       (or (<=
                                                                            z
                                                                            5.2e+151)
                                                                           (and (not
                                                                                 (<=
                                                                                  z
                                                                                  2.1e+156))
                                                                                (or (<=
                                                                                     z
                                                                                     6.6e+156)
                                                                                    (and (not
                                                                                          (<=
                                                                                           z
                                                                                           5.4e+169))
                                                                                         (or (<=
                                                                                              z
                                                                                              2.3e+182)
                                                                                             (and (not
                                                                                                   (<=
                                                                                                    z
                                                                                                    2.3e+185))
                                                                                                  (or (<=
                                                                                                       z
                                                                                                       2.7e+191)
                                                                                                      (and (not
                                                                                                            (<=
                                                                                                             z
                                                                                                             8.4e+210))
                                                                                                           (or (<=
                                                                                                                z
                                                                                                                9.2e+230)
                                                                                                               (and (not
                                                                                                                     (<=
                                                                                                                      z
                                                                                                                      7.2e+241))
                                                                                                                    (or (<=
                                                                                                                         z
                                                                                                                         8.2e+264)
                                                                                                                        (and (not
                                                                                                                              (<=
                                                                                                                               z
                                                                                                                               9.5e+269))
                                                                                                                             (or (<=
                                                                                                                                  z
                                                                                                                                  3.5e+270)
                                                                                                                                 (and (not
                                                                                                                                       (<=
                                                                                                                                        z
                                                                                                                                        7.4e+282))
                                                                                                                                      (or (<=
                                                                                                                                           z
                                                                                                                                           2.9e+283)
                                                                                                                                          (and (not
                                                                                                                                                (<=
                                                                                                                                                 z
                                                                                                                                                 9e+288))
                                                                                                                                               (<=
                                                                                                                                                z
                                                                                                                                                7.2e+291)))))))))))))))))))))))))))))
               t_0
               (* z (- y))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = y * (1.0 - z);
	double tmp;
	if (z <= -2.15e-13) {
		tmp = t_1;
	} else if (z <= 3.5e-16) {
		tmp = x + y;
	} else if (z <= 320000.0) {
		tmp = t_1;
	} else if (z <= 1250000.0) {
		tmp = t_0;
	} else if (z <= 3.9e+40) {
		tmp = t_1;
	} else if ((z <= 4.8e+45) || (!(z <= 8e+56) && ((z <= 8.2e+69) || (!(z <= 5e+83) && ((z <= 6.6e+97) || (!(z <= 4.1e+98) && ((z <= 1.1e+102) || (!(z <= 1.5e+118) && ((z <= 4.2e+123) || (!(z <= 1.7e+127) && ((z <= 1.4e+142) || (!(z <= 1.55e+150) && ((z <= 5.2e+151) || (!(z <= 2.1e+156) && ((z <= 6.6e+156) || (!(z <= 5.4e+169) && ((z <= 2.3e+182) || (!(z <= 2.3e+185) && ((z <= 2.7e+191) || (!(z <= 8.4e+210) && ((z <= 9.2e+230) || (!(z <= 7.2e+241) && ((z <= 8.2e+264) || (!(z <= 9.5e+269) && ((z <= 3.5e+270) || (!(z <= 7.4e+282) && ((z <= 2.9e+283) || (!(z <= 9e+288) && (z <= 7.2e+291))))))))))))))))))))))))))))) {
		tmp = t_0;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * -z
    t_1 = y * (1.0d0 - z)
    if (z <= (-2.15d-13)) then
        tmp = t_1
    else if (z <= 3.5d-16) then
        tmp = x + y
    else if (z <= 320000.0d0) then
        tmp = t_1
    else if (z <= 1250000.0d0) then
        tmp = t_0
    else if (z <= 3.9d+40) then
        tmp = t_1
    else if ((z <= 4.8d+45) .or. (.not. (z <= 8d+56)) .and. (z <= 8.2d+69) .or. (.not. (z <= 5d+83)) .and. (z <= 6.6d+97) .or. (.not. (z <= 4.1d+98)) .and. (z <= 1.1d+102) .or. (.not. (z <= 1.5d+118)) .and. (z <= 4.2d+123) .or. (.not. (z <= 1.7d+127)) .and. (z <= 1.4d+142) .or. (.not. (z <= 1.55d+150)) .and. (z <= 5.2d+151) .or. (.not. (z <= 2.1d+156)) .and. (z <= 6.6d+156) .or. (.not. (z <= 5.4d+169)) .and. (z <= 2.3d+182) .or. (.not. (z <= 2.3d+185)) .and. (z <= 2.7d+191) .or. (.not. (z <= 8.4d+210)) .and. (z <= 9.2d+230) .or. (.not. (z <= 7.2d+241)) .and. (z <= 8.2d+264) .or. (.not. (z <= 9.5d+269)) .and. (z <= 3.5d+270) .or. (.not. (z <= 7.4d+282)) .and. (z <= 2.9d+283) .or. (.not. (z <= 9d+288)) .and. (z <= 7.2d+291)) then
        tmp = t_0
    else
        tmp = z * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = y * (1.0 - z);
	double tmp;
	if (z <= -2.15e-13) {
		tmp = t_1;
	} else if (z <= 3.5e-16) {
		tmp = x + y;
	} else if (z <= 320000.0) {
		tmp = t_1;
	} else if (z <= 1250000.0) {
		tmp = t_0;
	} else if (z <= 3.9e+40) {
		tmp = t_1;
	} else if ((z <= 4.8e+45) || (!(z <= 8e+56) && ((z <= 8.2e+69) || (!(z <= 5e+83) && ((z <= 6.6e+97) || (!(z <= 4.1e+98) && ((z <= 1.1e+102) || (!(z <= 1.5e+118) && ((z <= 4.2e+123) || (!(z <= 1.7e+127) && ((z <= 1.4e+142) || (!(z <= 1.55e+150) && ((z <= 5.2e+151) || (!(z <= 2.1e+156) && ((z <= 6.6e+156) || (!(z <= 5.4e+169) && ((z <= 2.3e+182) || (!(z <= 2.3e+185) && ((z <= 2.7e+191) || (!(z <= 8.4e+210) && ((z <= 9.2e+230) || (!(z <= 7.2e+241) && ((z <= 8.2e+264) || (!(z <= 9.5e+269) && ((z <= 3.5e+270) || (!(z <= 7.4e+282) && ((z <= 2.9e+283) || (!(z <= 9e+288) && (z <= 7.2e+291))))))))))))))))))))))))))))) {
		tmp = t_0;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	t_1 = y * (1.0 - z)
	tmp = 0
	if z <= -2.15e-13:
		tmp = t_1
	elif z <= 3.5e-16:
		tmp = x + y
	elif z <= 320000.0:
		tmp = t_1
	elif z <= 1250000.0:
		tmp = t_0
	elif z <= 3.9e+40:
		tmp = t_1
	elif (z <= 4.8e+45) or (not (z <= 8e+56) and ((z <= 8.2e+69) or (not (z <= 5e+83) and ((z <= 6.6e+97) or (not (z <= 4.1e+98) and ((z <= 1.1e+102) or (not (z <= 1.5e+118) and ((z <= 4.2e+123) or (not (z <= 1.7e+127) and ((z <= 1.4e+142) or (not (z <= 1.55e+150) and ((z <= 5.2e+151) or (not (z <= 2.1e+156) and ((z <= 6.6e+156) or (not (z <= 5.4e+169) and ((z <= 2.3e+182) or (not (z <= 2.3e+185) and ((z <= 2.7e+191) or (not (z <= 8.4e+210) and ((z <= 9.2e+230) or (not (z <= 7.2e+241) and ((z <= 8.2e+264) or (not (z <= 9.5e+269) and ((z <= 3.5e+270) or (not (z <= 7.4e+282) and ((z <= 2.9e+283) or (not (z <= 9e+288) and (z <= 7.2e+291)))))))))))))))))))))))))))):
		tmp = t_0
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	t_1 = Float64(y * Float64(1.0 - z))
	tmp = 0.0
	if (z <= -2.15e-13)
		tmp = t_1;
	elseif (z <= 3.5e-16)
		tmp = Float64(x + y);
	elseif (z <= 320000.0)
		tmp = t_1;
	elseif (z <= 1250000.0)
		tmp = t_0;
	elseif (z <= 3.9e+40)
		tmp = t_1;
	elseif ((z <= 4.8e+45) || (!(z <= 8e+56) && ((z <= 8.2e+69) || (!(z <= 5e+83) && ((z <= 6.6e+97) || (!(z <= 4.1e+98) && ((z <= 1.1e+102) || (!(z <= 1.5e+118) && ((z <= 4.2e+123) || (!(z <= 1.7e+127) && ((z <= 1.4e+142) || (!(z <= 1.55e+150) && ((z <= 5.2e+151) || (!(z <= 2.1e+156) && ((z <= 6.6e+156) || (!(z <= 5.4e+169) && ((z <= 2.3e+182) || (!(z <= 2.3e+185) && ((z <= 2.7e+191) || (!(z <= 8.4e+210) && ((z <= 9.2e+230) || (!(z <= 7.2e+241) && ((z <= 8.2e+264) || (!(z <= 9.5e+269) && ((z <= 3.5e+270) || (!(z <= 7.4e+282) && ((z <= 2.9e+283) || (!(z <= 9e+288) && (z <= 7.2e+291)))))))))))))))))))))))))))))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	t_1 = y * (1.0 - z);
	tmp = 0.0;
	if (z <= -2.15e-13)
		tmp = t_1;
	elseif (z <= 3.5e-16)
		tmp = x + y;
	elseif (z <= 320000.0)
		tmp = t_1;
	elseif (z <= 1250000.0)
		tmp = t_0;
	elseif (z <= 3.9e+40)
		tmp = t_1;
	elseif ((z <= 4.8e+45) || (~((z <= 8e+56)) && ((z <= 8.2e+69) || (~((z <= 5e+83)) && ((z <= 6.6e+97) || (~((z <= 4.1e+98)) && ((z <= 1.1e+102) || (~((z <= 1.5e+118)) && ((z <= 4.2e+123) || (~((z <= 1.7e+127)) && ((z <= 1.4e+142) || (~((z <= 1.55e+150)) && ((z <= 5.2e+151) || (~((z <= 2.1e+156)) && ((z <= 6.6e+156) || (~((z <= 5.4e+169)) && ((z <= 2.3e+182) || (~((z <= 2.3e+185)) && ((z <= 2.7e+191) || (~((z <= 8.4e+210)) && ((z <= 9.2e+230) || (~((z <= 7.2e+241)) && ((z <= 8.2e+264) || (~((z <= 9.5e+269)) && ((z <= 3.5e+270) || (~((z <= 7.4e+282)) && ((z <= 2.9e+283) || (~((z <= 9e+288)) && (z <= 7.2e+291)))))))))))))))))))))))))))))
		tmp = t_0;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.15e-13], t$95$1, If[LessEqual[z, 3.5e-16], N[(x + y), $MachinePrecision], If[LessEqual[z, 320000.0], t$95$1, If[LessEqual[z, 1250000.0], t$95$0, If[LessEqual[z, 3.9e+40], t$95$1, If[Or[LessEqual[z, 4.8e+45], And[N[Not[LessEqual[z, 8e+56]], $MachinePrecision], Or[LessEqual[z, 8.2e+69], And[N[Not[LessEqual[z, 5e+83]], $MachinePrecision], Or[LessEqual[z, 6.6e+97], And[N[Not[LessEqual[z, 4.1e+98]], $MachinePrecision], Or[LessEqual[z, 1.1e+102], And[N[Not[LessEqual[z, 1.5e+118]], $MachinePrecision], Or[LessEqual[z, 4.2e+123], And[N[Not[LessEqual[z, 1.7e+127]], $MachinePrecision], Or[LessEqual[z, 1.4e+142], And[N[Not[LessEqual[z, 1.55e+150]], $MachinePrecision], Or[LessEqual[z, 5.2e+151], And[N[Not[LessEqual[z, 2.1e+156]], $MachinePrecision], Or[LessEqual[z, 6.6e+156], And[N[Not[LessEqual[z, 5.4e+169]], $MachinePrecision], Or[LessEqual[z, 2.3e+182], And[N[Not[LessEqual[z, 2.3e+185]], $MachinePrecision], Or[LessEqual[z, 2.7e+191], And[N[Not[LessEqual[z, 8.4e+210]], $MachinePrecision], Or[LessEqual[z, 9.2e+230], And[N[Not[LessEqual[z, 7.2e+241]], $MachinePrecision], Or[LessEqual[z, 8.2e+264], And[N[Not[LessEqual[z, 9.5e+269]], $MachinePrecision], Or[LessEqual[z, 3.5e+270], And[N[Not[LessEqual[z, 7.4e+282]], $MachinePrecision], Or[LessEqual[z, 2.9e+283], And[N[Not[LessEqual[z, 9e+288]], $MachinePrecision], LessEqual[z, 7.2e+291]]]]]]]]]]]]]]]]]]]]]]]]]]]]], t$95$0, N[(z * (-y)), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.1499999999999999e-13 or 3.50000000000000017e-16 < z < 3.2e5 or 1.25e6 < z < 3.9000000000000001e40

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 45.5%

      \[\leadsto \color{blue}{y \cdot \left(1 - z\right)} \]

   if -2.1499999999999999e-13 < z < 3.50000000000000017e-16

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 100.0%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{y + x} \]

   if 3.2e5 < z < 1.25e6 or 3.9000000000000001e40 < z < 4.79999999999999979e45 or 8.00000000000000074e56 < z < 8.1999999999999998e69 or 5.00000000000000029e83 < z < 6.6000000000000003e97 or 4.1e98 < z < 1.10000000000000004e102 or 1.5e118 < z < 4.19999999999999988e123 or 1.69999999999999989e127 < z < 1.4e142 or 1.55000000000000007e150 < z < 5.20000000000000026e151 or 2.09999999999999981e156 < z < 6.5999999999999997e156 or 5.39999999999999981e169 < z < 2.3e182 or 2.3000000000000001e185 < z < 2.69999999999999996e191 or 8.3999999999999994e210 < z < 9.1999999999999993e230 or 7.19999999999999966e241 < z < 8.1999999999999999e264 or 9.50000000000000044e269 < z < 3.4999999999999999e270 or 7.4000000000000004e282 < z < 2.8999999999999999e283 or 9.00000000000000034e288 < z < 7.1999999999999995e291

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 96.8%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(x + y\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 96.8%

         \[\leadsto \color{blue}{-z \cdot \left(x + y\right)} \]

      2. distribute-lft-neg-out 96.8%

         \[\leadsto \color{blue}{\left(-z\right) \cdot \left(x + y\right)} \]

      3. *-commutative 96.8%

         \[\leadsto \color{blue}{\left(x + y\right) \cdot \left(-z\right)} \]

      4. +-commutative 96.8%

         \[\leadsto \color{blue}{\left(y + x\right)} \cdot \left(-z\right) \]

   5. Simplified 96.8%

      \[\leadsto \color{blue}{\left(y + x\right) \cdot \left(-z\right)} \]

   6. Taylor expanded in y around 0 44.6%

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

      1. associate-*r* 44.6%

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot z} \]

      2. mul-1-neg 44.6%

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

   8. Simplified 44.6%

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

   if 4.79999999999999979e45 < z < 8.00000000000000074e56 or 8.1999999999999998e69 < z < 5.00000000000000029e83 or 6.6000000000000003e97 < z < 4.1e98 or 1.10000000000000004e102 < z < 1.5e118 or 4.19999999999999988e123 < z < 1.69999999999999989e127 or 1.4e142 < z < 1.55000000000000007e150 or 5.20000000000000026e151 < z < 2.09999999999999981e156 or 6.5999999999999997e156 < z < 5.39999999999999981e169 or 2.3e182 < z < 2.3000000000000001e185 or 2.69999999999999996e191 < z < 8.3999999999999994e210 or 9.1999999999999993e230 < z < 7.19999999999999966e241 or 8.1999999999999999e264 < z < 9.50000000000000044e269 or 3.4999999999999999e270 < z < 7.4000000000000004e282 or 2.8999999999999999e283 < z < 9.00000000000000034e288 or 7.1999999999999995e291 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(x + y\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 100.0%

         \[\leadsto \color{blue}{-z \cdot \left(x + y\right)} \]

      2. distribute-lft-neg-out 100.0%

         \[\leadsto \color{blue}{\left(-z\right) \cdot \left(x + y\right)} \]

      3. *-commutative 100.0%

         \[\leadsto \color{blue}{\left(x + y\right) \cdot \left(-z\right)} \]

      4. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(y + x\right)} \cdot \left(-z\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\left(y + x\right) \cdot \left(-z\right)} \]

   6. Taylor expanded in y around inf 48.1%

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

      1. associate-*r* 48.1%

         \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot z} \]

      2. mul-1-neg 48.1%

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

   8. Simplified 48.1%

      \[\leadsto \color{blue}{\left(-y\right) \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-16}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 320000:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 1250000:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+40}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+45} \lor \neg \left(z \leq 8 \cdot 10^{+56}\right) \land \left(z \leq 8.2 \cdot 10^{+69} \lor \neg \left(z \leq 5 \cdot 10^{+83}\right) \land \left(z \leq 6.6 \cdot 10^{+97} \lor \neg \left(z \leq 4.1 \cdot 10^{+98}\right) \land \left(z \leq 1.1 \cdot 10^{+102} \lor \neg \left(z \leq 1.5 \cdot 10^{+118}\right) \land \left(z \leq 4.2 \cdot 10^{+123} \lor \neg \left(z \leq 1.7 \cdot 10^{+127}\right) \land \left(z \leq 1.4 \cdot 10^{+142} \lor \neg \left(z \leq 1.55 \cdot 10^{+150}\right) \land \left(z \leq 5.2 \cdot 10^{+151} \lor \neg \left(z \leq 2.1 \cdot 10^{+156}\right) \land \left(z \leq 6.6 \cdot 10^{+156} \lor \neg \left(z \leq 5.4 \cdot 10^{+169}\right) \land \left(z \leq 2.3 \cdot 10^{+182} \lor \neg \left(z \leq 2.3 \cdot 10^{+185}\right) \land \left(z \leq 2.7 \cdot 10^{+191} \lor \neg \left(z \leq 8.4 \cdot 10^{+210}\right) \land \left(z \leq 9.2 \cdot 10^{+230} \lor \neg \left(z \leq 7.2 \cdot 10^{+241}\right) \land \left(z \leq 8.2 \cdot 10^{+264} \lor \neg \left(z \leq 9.5 \cdot 10^{+269}\right) \land \left(z \leq 3.5 \cdot 10^{+270} \lor \neg \left(z \leq 7.4 \cdot 10^{+282}\right) \land \left(z \leq 2.9 \cdot 10^{+283} \lor \neg \left(z \leq 9 \cdot 10^{+288}\right) \land z \leq 7.2 \cdot 10^{+291}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.3% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-y\right)\\ t_1 := x \cdot \left(1 - z\right)\\ t_2 := y \cdot \left(1 - z\right)\\ t_3 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-16}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 0.092:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1250000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+42}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+58}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+70}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+83}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+97}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+100}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+102}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+118}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+124}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+126}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+139}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+150}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+154}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+156}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+156}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+174}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+180}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+185}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+191}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+211}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+231}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+241}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+266}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+270} \lor \neg \left(z \leq 2.8 \cdot 10^{+270}\right) \land \left(z \leq 1.6 \cdot 10^{+281} \lor \neg \left(z \leq 2.05 \cdot 10^{+283} \lor \neg \left(z \leq 2.65 \cdot 10^{+289}\right) \land z \leq 2.8 \cdot 10^{+295}\right)\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- y)))
        (t_1 (* x (- 1.0 z)))
        (t_2 (* y (- 1.0 z)))
        (t_3 (* x (- z))))
   (if (<= z -2.15e-13)
     t_2
     (if (<= z 3.5e-16)
       (+ x y)
       (if (<= z 0.092)
         t_2
         (if (<= z 1250000.0)
           t_1
           (if (<= z 2.5e+33)
             t_2
             (if (<= z 1.4e+42)
               t_3
               (if (<= z 1.45e+58)
                 t_0
                 (if (<= z 7.5e+70)
                   t_3
                   (if (<= z 2.9e+83)
                     t_0
                     (if (<= z 3.5e+97)
                       t_3
                       (if (<= z 4.8e+100)
                         t_0
                         (if (<= z 1.55e+102)
                           t_3
                           (if (<= z 2e+118)
                             t_0
                             (if (<= z 1.5e+124)
                               t_3
                               (if (<= z 1.45e+126)
                                 t_0
                                 (if (<= z 4.4e+139)
                                   t_3
                                   (if (<= z 4.2e+150)
                                     t_0
                                     (if (<= z 1.65e+154)
                                       t_3
                                       (if (<= z 2e+156)
                                         t_0
                                         (if (<= z 4.5e+156)
                                           t_3
                                           (if (<= z 1.9e+174)
                                             t_0
                                             (if (<= z 4.6e+180)
                                               t_3
                                               (if (<= z 2.3e+185)
                                                 t_0
                                                 (if (<= z 2.5e+191)
                                                   t_3
                                                   (if (<= z 1.85e+211)
                                                     t_0
                                                     (if (<= z 4.7e+231)
                                                       t_3
                                                       (if (<= z 1.4e+241)
                                                         t_0
                                                         (if (<= z 2.6e+266)
                                                           t_1
                                                           (if (or (<=
                                                                    z
                                                                    1.05e+270)
                                                                   (and (not
                                                                         (<=
                                                                          z
                                                                          2.8e+270))
                                                                        (or (<=
                                                                             z
                                                                             1.6e+281)
                                                                            (not
                                                                             (or (<=
                                                                                  z
                                                                                  2.05e+283)
                                                                                 (and (not
                                                                                       (<=
                                                                                        z
                                                                                        2.65e+289))
                                                                                      (<=
                                                                                       z
                                                                                       2.8e+295)))))))
                                                             t_0
                                                             t_3)))))))))))))))))))))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -y;
	double t_1 = x * (1.0 - z);
	double t_2 = y * (1.0 - z);
	double t_3 = x * -z;
	double tmp;
	if (z <= -2.15e-13) {
		tmp = t_2;
	} else if (z <= 3.5e-16) {
		tmp = x + y;
	} else if (z <= 0.092) {
		tmp = t_2;
	} else if (z <= 1250000.0) {
		tmp = t_1;
	} else if (z <= 2.5e+33) {
		tmp = t_2;
	} else if (z <= 1.4e+42) {
		tmp = t_3;
	} else if (z <= 1.45e+58) {
		tmp = t_0;
	} else if (z <= 7.5e+70) {
		tmp = t_3;
	} else if (z <= 2.9e+83) {
		tmp = t_0;
	} else if (z <= 3.5e+97) {
		tmp = t_3;
	} else if (z <= 4.8e+100) {
		tmp = t_0;
	} else if (z <= 1.55e+102) {
		tmp = t_3;
	} else if (z <= 2e+118) {
		tmp = t_0;
	} else if (z <= 1.5e+124) {
		tmp = t_3;
	} else if (z <= 1.45e+126) {
		tmp = t_0;
	} else if (z <= 4.4e+139) {
		tmp = t_3;
	} else if (z <= 4.2e+150) {
		tmp = t_0;
	} else if (z <= 1.65e+154) {
		tmp = t_3;
	} else if (z <= 2e+156) {
		tmp = t_0;
	} else if (z <= 4.5e+156) {
		tmp = t_3;
	} else if (z <= 1.9e+174) {
		tmp = t_0;
	} else if (z <= 4.6e+180) {
		tmp = t_3;
	} else if (z <= 2.3e+185) {
		tmp = t_0;
	} else if (z <= 2.5e+191) {
		tmp = t_3;
	} else if (z <= 1.85e+211) {
		tmp = t_0;
	} else if (z <= 4.7e+231) {
		tmp = t_3;
	} else if (z <= 1.4e+241) {
		tmp = t_0;
	} else if (z <= 2.6e+266) {
		tmp = t_1;
	} else if ((z <= 1.05e+270) || (!(z <= 2.8e+270) && ((z <= 1.6e+281) || !((z <= 2.05e+283) || (!(z <= 2.65e+289) && (z <= 2.8e+295)))))) {
		tmp = t_0;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = z * -y
    t_1 = x * (1.0d0 - z)
    t_2 = y * (1.0d0 - z)
    t_3 = x * -z
    if (z <= (-2.15d-13)) then
        tmp = t_2
    else if (z <= 3.5d-16) then
        tmp = x + y
    else if (z <= 0.092d0) then
        tmp = t_2
    else if (z <= 1250000.0d0) then
        tmp = t_1
    else if (z <= 2.5d+33) then
        tmp = t_2
    else if (z <= 1.4d+42) then
        tmp = t_3
    else if (z <= 1.45d+58) then
        tmp = t_0
    else if (z <= 7.5d+70) then
        tmp = t_3
    else if (z <= 2.9d+83) then
        tmp = t_0
    else if (z <= 3.5d+97) then
        tmp = t_3
    else if (z <= 4.8d+100) then
        tmp = t_0
    else if (z <= 1.55d+102) then
        tmp = t_3
    else if (z <= 2d+118) then
        tmp = t_0
    else if (z <= 1.5d+124) then
        tmp = t_3
    else if (z <= 1.45d+126) then
        tmp = t_0
    else if (z <= 4.4d+139) then
        tmp = t_3
    else if (z <= 4.2d+150) then
        tmp = t_0
    else if (z <= 1.65d+154) then
        tmp = t_3
    else if (z <= 2d+156) then
        tmp = t_0
    else if (z <= 4.5d+156) then
        tmp = t_3
    else if (z <= 1.9d+174) then
        tmp = t_0
    else if (z <= 4.6d+180) then
        tmp = t_3
    else if (z <= 2.3d+185) then
        tmp = t_0
    else if (z <= 2.5d+191) then
        tmp = t_3
    else if (z <= 1.85d+211) then
        tmp = t_0
    else if (z <= 4.7d+231) then
        tmp = t_3
    else if (z <= 1.4d+241) then
        tmp = t_0
    else if (z <= 2.6d+266) then
        tmp = t_1
    else if ((z <= 1.05d+270) .or. (.not. (z <= 2.8d+270)) .and. (z <= 1.6d+281) .or. (.not. (z <= 2.05d+283) .or. (.not. (z <= 2.65d+289)) .and. (z <= 2.8d+295))) then
        tmp = t_0
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -y;
	double t_1 = x * (1.0 - z);
	double t_2 = y * (1.0 - z);
	double t_3 = x * -z;
	double tmp;
	if (z <= -2.15e-13) {
		tmp = t_2;
	} else if (z <= 3.5e-16) {
		tmp = x + y;
	} else if (z <= 0.092) {
		tmp = t_2;
	} else if (z <= 1250000.0) {
		tmp = t_1;
	} else if (z <= 2.5e+33) {
		tmp = t_2;
	} else if (z <= 1.4e+42) {
		tmp = t_3;
	} else if (z <= 1.45e+58) {
		tmp = t_0;
	} else if (z <= 7.5e+70) {
		tmp = t_3;
	} else if (z <= 2.9e+83) {
		tmp = t_0;
	} else if (z <= 3.5e+97) {
		tmp = t_3;
	} else if (z <= 4.8e+100) {
		tmp = t_0;
	} else if (z <= 1.55e+102) {
		tmp = t_3;
	} else if (z <= 2e+118) {
		tmp = t_0;
	} else if (z <= 1.5e+124) {
		tmp = t_3;
	} else if (z <= 1.45e+126) {
		tmp = t_0;
	} else if (z <= 4.4e+139) {
		tmp = t_3;
	} else if (z <= 4.2e+150) {
		tmp = t_0;
	} else if (z <= 1.65e+154) {
		tmp = t_3;
	} else if (z <= 2e+156) {
		tmp = t_0;
	} else if (z <= 4.5e+156) {
		tmp = t_3;
	} else if (z <= 1.9e+174) {
		tmp = t_0;
	} else if (z <= 4.6e+180) {
		tmp = t_3;
	} else if (z <= 2.3e+185) {
		tmp = t_0;
	} else if (z <= 2.5e+191) {
		tmp = t_3;
	} else if (z <= 1.85e+211) {
		tmp = t_0;
	} else if (z <= 4.7e+231) {
		tmp = t_3;
	} else if (z <= 1.4e+241) {
		tmp = t_0;
	} else if (z <= 2.6e+266) {
		tmp = t_1;
	} else if ((z <= 1.05e+270) || (!(z <= 2.8e+270) && ((z <= 1.6e+281) || !((z <= 2.05e+283) || (!(z <= 2.65e+289) && (z <= 2.8e+295)))))) {
		tmp = t_0;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -y
	t_1 = x * (1.0 - z)
	t_2 = y * (1.0 - z)
	t_3 = x * -z
	tmp = 0
	if z <= -2.15e-13:
		tmp = t_2
	elif z <= 3.5e-16:
		tmp = x + y
	elif z <= 0.092:
		tmp = t_2
	elif z <= 1250000.0:
		tmp = t_1
	elif z <= 2.5e+33:
		tmp = t_2
	elif z <= 1.4e+42:
		tmp = t_3
	elif z <= 1.45e+58:
		tmp = t_0
	elif z <= 7.5e+70:
		tmp = t_3
	elif z <= 2.9e+83:
		tmp = t_0
	elif z <= 3.5e+97:
		tmp = t_3
	elif z <= 4.8e+100:
		tmp = t_0
	elif z <= 1.55e+102:
		tmp = t_3
	elif z <= 2e+118:
		tmp = t_0
	elif z <= 1.5e+124:
		tmp = t_3
	elif z <= 1.45e+126:
		tmp = t_0
	elif z <= 4.4e+139:
		tmp = t_3
	elif z <= 4.2e+150:
		tmp = t_0
	elif z <= 1.65e+154:
		tmp = t_3
	elif z <= 2e+156:
		tmp = t_0
	elif z <= 4.5e+156:
		tmp = t_3
	elif z <= 1.9e+174:
		tmp = t_0
	elif z <= 4.6e+180:
		tmp = t_3
	elif z <= 2.3e+185:
		tmp = t_0
	elif z <= 2.5e+191:
		tmp = t_3
	elif z <= 1.85e+211:
		tmp = t_0
	elif z <= 4.7e+231:
		tmp = t_3
	elif z <= 1.4e+241:
		tmp = t_0
	elif z <= 2.6e+266:
		tmp = t_1
	elif (z <= 1.05e+270) or (not (z <= 2.8e+270) and ((z <= 1.6e+281) or not ((z <= 2.05e+283) or (not (z <= 2.65e+289) and (z <= 2.8e+295))))):
		tmp = t_0
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-y))
	t_1 = Float64(x * Float64(1.0 - z))
	t_2 = Float64(y * Float64(1.0 - z))
	t_3 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -2.15e-13)
		tmp = t_2;
	elseif (z <= 3.5e-16)
		tmp = Float64(x + y);
	elseif (z <= 0.092)
		tmp = t_2;
	elseif (z <= 1250000.0)
		tmp = t_1;
	elseif (z <= 2.5e+33)
		tmp = t_2;
	elseif (z <= 1.4e+42)
		tmp = t_3;
	elseif (z <= 1.45e+58)
		tmp = t_0;
	elseif (z <= 7.5e+70)
		tmp = t_3;
	elseif (z <= 2.9e+83)
		tmp = t_0;
	elseif (z <= 3.5e+97)
		tmp = t_3;
	elseif (z <= 4.8e+100)
		tmp = t_0;
	elseif (z <= 1.55e+102)
		tmp = t_3;
	elseif (z <= 2e+118)
		tmp = t_0;
	elseif (z <= 1.5e+124)
		tmp = t_3;
	elseif (z <= 1.45e+126)
		tmp = t_0;
	elseif (z <= 4.4e+139)
		tmp = t_3;
	elseif (z <= 4.2e+150)
		tmp = t_0;
	elseif (z <= 1.65e+154)
		tmp = t_3;
	elseif (z <= 2e+156)
		tmp = t_0;
	elseif (z <= 4.5e+156)
		tmp = t_3;
	elseif (z <= 1.9e+174)
		tmp = t_0;
	elseif (z <= 4.6e+180)
		tmp = t_3;
	elseif (z <= 2.3e+185)
		tmp = t_0;
	elseif (z <= 2.5e+191)
		tmp = t_3;
	elseif (z <= 1.85e+211)
		tmp = t_0;
	elseif (z <= 4.7e+231)
		tmp = t_3;
	elseif (z <= 1.4e+241)
		tmp = t_0;
	elseif (z <= 2.6e+266)
		tmp = t_1;
	elseif ((z <= 1.05e+270) || (!(z <= 2.8e+270) && ((z <= 1.6e+281) || !((z <= 2.05e+283) || (!(z <= 2.65e+289) && (z <= 2.8e+295))))))
		tmp = t_0;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -y;
	t_1 = x * (1.0 - z);
	t_2 = y * (1.0 - z);
	t_3 = x * -z;
	tmp = 0.0;
	if (z <= -2.15e-13)
		tmp = t_2;
	elseif (z <= 3.5e-16)
		tmp = x + y;
	elseif (z <= 0.092)
		tmp = t_2;
	elseif (z <= 1250000.0)
		tmp = t_1;
	elseif (z <= 2.5e+33)
		tmp = t_2;
	elseif (z <= 1.4e+42)
		tmp = t_3;
	elseif (z <= 1.45e+58)
		tmp = t_0;
	elseif (z <= 7.5e+70)
		tmp = t_3;
	elseif (z <= 2.9e+83)
		tmp = t_0;
	elseif (z <= 3.5e+97)
		tmp = t_3;
	elseif (z <= 4.8e+100)
		tmp = t_0;
	elseif (z <= 1.55e+102)
		tmp = t_3;
	elseif (z <= 2e+118)
		tmp = t_0;
	elseif (z <= 1.5e+124)
		tmp = t_3;
	elseif (z <= 1.45e+126)
		tmp = t_0;
	elseif (z <= 4.4e+139)
		tmp = t_3;
	elseif (z <= 4.2e+150)
		tmp = t_0;
	elseif (z <= 1.65e+154)
		tmp = t_3;
	elseif (z <= 2e+156)
		tmp = t_0;
	elseif (z <= 4.5e+156)
		tmp = t_3;
	elseif (z <= 1.9e+174)
		tmp = t_0;
	elseif (z <= 4.6e+180)
		tmp = t_3;
	elseif (z <= 2.3e+185)
		tmp = t_0;
	elseif (z <= 2.5e+191)
		tmp = t_3;
	elseif (z <= 1.85e+211)
		tmp = t_0;
	elseif (z <= 4.7e+231)
		tmp = t_3;
	elseif (z <= 1.4e+241)
		tmp = t_0;
	elseif (z <= 2.6e+266)
		tmp = t_1;
	elseif ((z <= 1.05e+270) || (~((z <= 2.8e+270)) && ((z <= 1.6e+281) || ~(((z <= 2.05e+283) || (~((z <= 2.65e+289)) && (z <= 2.8e+295)))))))
		tmp = t_0;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-y)), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -2.15e-13], t$95$2, If[LessEqual[z, 3.5e-16], N[(x + y), $MachinePrecision], If[LessEqual[z, 0.092], t$95$2, If[LessEqual[z, 1250000.0], t$95$1, If[LessEqual[z, 2.5e+33], t$95$2, If[LessEqual[z, 1.4e+42], t$95$3, If[LessEqual[z, 1.45e+58], t$95$0, If[LessEqual[z, 7.5e+70], t$95$3, If[LessEqual[z, 2.9e+83], t$95$0, If[LessEqual[z, 3.5e+97], t$95$3, If[LessEqual[z, 4.8e+100], t$95$0, If[LessEqual[z, 1.55e+102], t$95$3, If[LessEqual[z, 2e+118], t$95$0, If[LessEqual[z, 1.5e+124], t$95$3, If[LessEqual[z, 1.45e+126], t$95$0, If[LessEqual[z, 4.4e+139], t$95$3, If[LessEqual[z, 4.2e+150], t$95$0, If[LessEqual[z, 1.65e+154], t$95$3, If[LessEqual[z, 2e+156], t$95$0, If[LessEqual[z, 4.5e+156], t$95$3, If[LessEqual[z, 1.9e+174], t$95$0, If[LessEqual[z, 4.6e+180], t$95$3, If[LessEqual[z, 2.3e+185], t$95$0, If[LessEqual[z, 2.5e+191], t$95$3, If[LessEqual[z, 1.85e+211], t$95$0, If[LessEqual[z, 4.7e+231], t$95$3, If[LessEqual[z, 1.4e+241], t$95$0, If[LessEqual[z, 2.6e+266], t$95$1, If[Or[LessEqual[z, 1.05e+270], And[N[Not[LessEqual[z, 2.8e+270]], $MachinePrecision], Or[LessEqual[z, 1.6e+281], N[Not[Or[LessEqual[z, 2.05e+283], And[N[Not[LessEqual[z, 2.65e+289]], $MachinePrecision], LessEqual[z, 2.8e+295]]]], $MachinePrecision]]]], t$95$0, t$95$3]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.1499999999999999e-13 or 3.50000000000000017e-16 < z < 0.091999999999999998 or 1.25e6 < z < 2.49999999999999986e33

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 45.5%

      \[\leadsto \color{blue}{y \cdot \left(1 - z\right)} \]

   if -2.1499999999999999e-13 < z < 3.50000000000000017e-16

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 100.0%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{y + x} \]

   if 0.091999999999999998 < z < 1.25e6 or 1.40000000000000013e241 < z < 2.60000000000000014e266

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 72.5%

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

      1. *-commutative 72.5%

         \[\leadsto \color{blue}{\left(1 - z\right) \cdot x} \]

   5. Simplified 72.5%

      \[\leadsto \color{blue}{\left(1 - z\right) \cdot x} \]

   if 2.49999999999999986e33 < z < 1.4e42 or 1.45000000000000001e58 < z < 7.50000000000000031e70 or 2.89999999999999999e83 < z < 3.5000000000000001e97 or 4.80000000000000023e100 < z < 1.54999999999999993e102 or 1.99999999999999993e118 < z < 1.5e124 or 1.44999999999999993e126 < z < 4.3999999999999999e139 or 4.19999999999999996e150 < z < 1.65e154 or 2e156 < z < 4.50000000000000031e156 or 1.9000000000000001e174 < z < 4.5999999999999998e180 or 2.3000000000000001e185 < z < 2.5000000000000001e191 or 1.85000000000000005e211 < z < 4.70000000000000006e231 or 1.05000000000000005e270 < z < 2.8000000000000001e270 or 1.6000000000000001e281 < z < 2.05000000000000002e283 or 2.65e289 < z < 2.8000000000000001e295

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(x + y\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 100.0%

         \[\leadsto \color{blue}{-z \cdot \left(x + y\right)} \]

      2. distribute-lft-neg-out 100.0%

         \[\leadsto \color{blue}{\left(-z\right) \cdot \left(x + y\right)} \]

      3. *-commutative 100.0%

         \[\leadsto \color{blue}{\left(x + y\right) \cdot \left(-z\right)} \]

      4. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(y + x\right)} \cdot \left(-z\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\left(y + x\right) \cdot \left(-z\right)} \]

   6. Taylor expanded in y around 0 40.1%

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

      1. associate-*r* 40.1%

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot z} \]

      2. mul-1-neg 40.1%

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

   8. Simplified 40.1%

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

   if 1.4e42 < z < 1.45000000000000001e58 or 7.50000000000000031e70 < z < 2.89999999999999999e83 or 3.5000000000000001e97 < z < 4.80000000000000023e100 or 1.54999999999999993e102 < z < 1.99999999999999993e118 or 1.5e124 < z < 1.44999999999999993e126 or 4.3999999999999999e139 < z < 4.19999999999999996e150 or 1.65e154 < z < 2e156 or 4.50000000000000031e156 < z < 1.9000000000000001e174 or 4.5999999999999998e180 < z < 2.3000000000000001e185 or 2.5000000000000001e191 < z < 1.85000000000000005e211 or 4.70000000000000006e231 < z < 1.40000000000000013e241 or 2.60000000000000014e266 < z < 1.05000000000000005e270 or 2.8000000000000001e270 < z < 1.6000000000000001e281 or 2.05000000000000002e283 < z < 2.65e289 or 2.8000000000000001e295 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(x + y\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 100.0%

         \[\leadsto \color{blue}{-z \cdot \left(x + y\right)} \]

      2. distribute-lft-neg-out 100.0%

         \[\leadsto \color{blue}{\left(-z\right) \cdot \left(x + y\right)} \]

      3. *-commutative 100.0%

         \[\leadsto \color{blue}{\left(x + y\right) \cdot \left(-z\right)} \]

      4. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(y + x\right)} \cdot \left(-z\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\left(y + x\right) \cdot \left(-z\right)} \]

   6. Taylor expanded in y around inf 48.1%

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

      1. associate-*r* 48.1%

         \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot z} \]

      2. mul-1-neg 48.1%

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

   8. Simplified 48.1%

      \[\leadsto \color{blue}{\left(-y\right) \cdot z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-16}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 0.092:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 1250000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+33}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+83}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+100}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+102}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+118}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+124}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+126}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+150}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+156}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+156}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+174}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+180}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+185}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+191}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+211}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+231}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+241}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+266}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+270} \lor \neg \left(z \leq 2.8 \cdot 10^{+270}\right) \land \left(z \leq 1.6 \cdot 10^{+281} \lor \neg \left(z \leq 2.05 \cdot 10^{+283} \lor \neg \left(z \leq 2.65 \cdot 10^{+289}\right) \land z \leq 2.8 \cdot 10^{+295}\right)\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.7% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-y\right)\\ \mathbf{if}\;z \leq -34:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1850000 \lor \neg \left(z \leq 8 \cdot 10^{+36}\right) \land \left(z \leq 1.05 \cdot 10^{+43} \lor \neg \left(z \leq 3.4 \cdot 10^{+59}\right) \land \left(z \leq 1.2 \cdot 10^{+72} \lor \neg \left(z \leq 2.7 \cdot 10^{+85}\right) \land \left(z \leq 3.2 \cdot 10^{+97} \lor \neg \left(z \leq 4.2 \cdot 10^{+99}\right) \land \left(z \leq 6.8 \cdot 10^{+100} \lor \neg \left(z \leq 5.2 \cdot 10^{+117}\right) \land \left(z \leq 2.2 \cdot 10^{+125} \lor \neg \left(z \leq 8.8 \cdot 10^{+126}\right) \land \left(z \leq 4.5 \cdot 10^{+142} \lor \neg \left(z \leq 3.4 \cdot 10^{+150}\right) \land \left(z \leq 2.55 \cdot 10^{+151} \lor \neg \left(z \leq 2.1 \cdot 10^{+156}\right) \land \left(z \leq 5.7 \cdot 10^{+156} \lor \neg \left(z \leq 1.05 \cdot 10^{+173}\right) \land \left(z \leq 4 \cdot 10^{+182} \lor \neg \left(z \leq 9.2 \cdot 10^{+184}\right) \land \left(z \leq 2.4 \cdot 10^{+191} \lor \neg \left(z \leq 2.05 \cdot 10^{+211}\right) \land \left(z \leq 4.2 \cdot 10^{+232} \lor \neg \left(z \leq 1.6 \cdot 10^{+241}\right) \land \left(z \leq 2.25 \cdot 10^{+265} \lor \neg \left(z \leq 10^{+270}\right) \land \left(z \leq 1.7 \cdot 10^{+270} \lor \neg \left(z \leq 1.95 \cdot 10^{+276}\right) \land \left(z \leq 1.35 \cdot 10^{+283} \lor \neg \left(z \leq 2.8 \cdot 10^{+289}\right) \land z \leq 2.05 \cdot 10^{+295}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- y))))
   (if (<= z -34.0)
     t_0
     (if (<= z 1.0)
       (+ x y)
       (if (or (<= z 1850000.0)
               (and (not (<= z 8e+36))
                    (or (<= z 1.05e+43)
                        (and (not (<= z 3.4e+59))
                             (or (<= z 1.2e+72)
                                 (and (not (<= z 2.7e+85))
                                      (or (<= z 3.2e+97)
                                          (and (not (<= z 4.2e+99))
                                               (or (<= z 6.8e+100)
                                                   (and (not (<= z 5.2e+117))
                                                        (or (<= z 2.2e+125)
                                                            (and (not
                                                                  (<=
                                                                   z
                                                                   8.8e+126))
                                                                 (or (<=
                                                                      z
                                                                      4.5e+142)
                                                                     (and (not
                                                                           (<=
                                                                            z
                                                                            3.4e+150))
                                                                          (or (<=
                                                                               z
                                                                               2.55e+151)
                                                                              (and (not
                                                                                    (<=
                                                                                     z
                                                                                     2.1e+156))
                                                                                   (or (<=
                                                                                        z
                                                                                        5.7e+156)
                                                                                       (and (not
                                                                                             (<=
                                                                                              z
                                                                                              1.05e+173))
                                                                                            (or (<=
                                                                                                 z
                                                                                                 4e+182)
                                                                                                (and (not
                                                                                                      (<=
                                                                                                       z
                                                                                                       9.2e+184))
                                                                                                     (or (<=
                                                                                                          z
                                                                                                          2.4e+191)
                                                                                                         (and (not
                                                                                                               (<=
                                                                                                                z
                                                                                                                2.05e+211))
                                                                                                              (or (<=
                                                                                                                   z
                                                                                                                   4.2e+232)
                                                                                                                  (and (not
                                                                                                                        (<=
                                                                                                                         z
                                                                                                                         1.6e+241))
                                                                                                                       (or (<=
                                                                                                                            z
                                                                                                                            2.25e+265)
                                                                                                                           (and (not
                                                                                                                                 (<=
                                                                                                                                  z
                                                                                                                                  1e+270))
                                                                                                                                (or (<=
                                                                                                                                     z
                                                                                                                                     1.7e+270)
                                                                                                                                    (and (not
                                                                                                                                          (<=
                                                                                                                                           z
                                                                                                                                           1.95e+276))
                                                                                                                                         (or (<=
                                                                                                                                              z
                                                                                                                                              1.35e+283)
                                                                                                                                             (and (not
                                                                                                                                                   (<=
                                                                                                                                                    z
                                                                                                                                                    2.8e+289))
                                                                                                                                                  (<=
                                                                                                                                                   z
                                                                                                                                                   2.05e+295)))))))))))))))))))))))))))))))
         (* x (- z))
         t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * -y;
	double tmp;
	if (z <= -34.0) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if ((z <= 1850000.0) || (!(z <= 8e+36) && ((z <= 1.05e+43) || (!(z <= 3.4e+59) && ((z <= 1.2e+72) || (!(z <= 2.7e+85) && ((z <= 3.2e+97) || (!(z <= 4.2e+99) && ((z <= 6.8e+100) || (!(z <= 5.2e+117) && ((z <= 2.2e+125) || (!(z <= 8.8e+126) && ((z <= 4.5e+142) || (!(z <= 3.4e+150) && ((z <= 2.55e+151) || (!(z <= 2.1e+156) && ((z <= 5.7e+156) || (!(z <= 1.05e+173) && ((z <= 4e+182) || (!(z <= 9.2e+184) && ((z <= 2.4e+191) || (!(z <= 2.05e+211) && ((z <= 4.2e+232) || (!(z <= 1.6e+241) && ((z <= 2.25e+265) || (!(z <= 1e+270) && ((z <= 1.7e+270) || (!(z <= 1.95e+276) && ((z <= 1.35e+283) || (!(z <= 2.8e+289) && (z <= 2.05e+295))))))))))))))))))))))))))))))) {
		tmp = x * -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * -y
    if (z <= (-34.0d0)) then
        tmp = t_0
    else if (z <= 1.0d0) then
        tmp = x + y
    else if ((z <= 1850000.0d0) .or. (.not. (z <= 8d+36)) .and. (z <= 1.05d+43) .or. (.not. (z <= 3.4d+59)) .and. (z <= 1.2d+72) .or. (.not. (z <= 2.7d+85)) .and. (z <= 3.2d+97) .or. (.not. (z <= 4.2d+99)) .and. (z <= 6.8d+100) .or. (.not. (z <= 5.2d+117)) .and. (z <= 2.2d+125) .or. (.not. (z <= 8.8d+126)) .and. (z <= 4.5d+142) .or. (.not. (z <= 3.4d+150)) .and. (z <= 2.55d+151) .or. (.not. (z <= 2.1d+156)) .and. (z <= 5.7d+156) .or. (.not. (z <= 1.05d+173)) .and. (z <= 4d+182) .or. (.not. (z <= 9.2d+184)) .and. (z <= 2.4d+191) .or. (.not. (z <= 2.05d+211)) .and. (z <= 4.2d+232) .or. (.not. (z <= 1.6d+241)) .and. (z <= 2.25d+265) .or. (.not. (z <= 1d+270)) .and. (z <= 1.7d+270) .or. (.not. (z <= 1.95d+276)) .and. (z <= 1.35d+283) .or. (.not. (z <= 2.8d+289)) .and. (z <= 2.05d+295)) then
        tmp = x * -z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -y;
	double tmp;
	if (z <= -34.0) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if ((z <= 1850000.0) || (!(z <= 8e+36) && ((z <= 1.05e+43) || (!(z <= 3.4e+59) && ((z <= 1.2e+72) || (!(z <= 2.7e+85) && ((z <= 3.2e+97) || (!(z <= 4.2e+99) && ((z <= 6.8e+100) || (!(z <= 5.2e+117) && ((z <= 2.2e+125) || (!(z <= 8.8e+126) && ((z <= 4.5e+142) || (!(z <= 3.4e+150) && ((z <= 2.55e+151) || (!(z <= 2.1e+156) && ((z <= 5.7e+156) || (!(z <= 1.05e+173) && ((z <= 4e+182) || (!(z <= 9.2e+184) && ((z <= 2.4e+191) || (!(z <= 2.05e+211) && ((z <= 4.2e+232) || (!(z <= 1.6e+241) && ((z <= 2.25e+265) || (!(z <= 1e+270) && ((z <= 1.7e+270) || (!(z <= 1.95e+276) && ((z <= 1.35e+283) || (!(z <= 2.8e+289) && (z <= 2.05e+295))))))))))))))))))))))))))))))) {
		tmp = x * -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -y
	tmp = 0
	if z <= -34.0:
		tmp = t_0
	elif z <= 1.0:
		tmp = x + y
	elif (z <= 1850000.0) or (not (z <= 8e+36) and ((z <= 1.05e+43) or (not (z <= 3.4e+59) and ((z <= 1.2e+72) or (not (z <= 2.7e+85) and ((z <= 3.2e+97) or (not (z <= 4.2e+99) and ((z <= 6.8e+100) or (not (z <= 5.2e+117) and ((z <= 2.2e+125) or (not (z <= 8.8e+126) and ((z <= 4.5e+142) or (not (z <= 3.4e+150) and ((z <= 2.55e+151) or (not (z <= 2.1e+156) and ((z <= 5.7e+156) or (not (z <= 1.05e+173) and ((z <= 4e+182) or (not (z <= 9.2e+184) and ((z <= 2.4e+191) or (not (z <= 2.05e+211) and ((z <= 4.2e+232) or (not (z <= 1.6e+241) and ((z <= 2.25e+265) or (not (z <= 1e+270) and ((z <= 1.7e+270) or (not (z <= 1.95e+276) and ((z <= 1.35e+283) or (not (z <= 2.8e+289) and (z <= 2.05e+295)))))))))))))))))))))))))))))):
		tmp = x * -z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-y))
	tmp = 0.0
	if (z <= -34.0)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = Float64(x + y);
	elseif ((z <= 1850000.0) || (!(z <= 8e+36) && ((z <= 1.05e+43) || (!(z <= 3.4e+59) && ((z <= 1.2e+72) || (!(z <= 2.7e+85) && ((z <= 3.2e+97) || (!(z <= 4.2e+99) && ((z <= 6.8e+100) || (!(z <= 5.2e+117) && ((z <= 2.2e+125) || (!(z <= 8.8e+126) && ((z <= 4.5e+142) || (!(z <= 3.4e+150) && ((z <= 2.55e+151) || (!(z <= 2.1e+156) && ((z <= 5.7e+156) || (!(z <= 1.05e+173) && ((z <= 4e+182) || (!(z <= 9.2e+184) && ((z <= 2.4e+191) || (!(z <= 2.05e+211) && ((z <= 4.2e+232) || (!(z <= 1.6e+241) && ((z <= 2.25e+265) || (!(z <= 1e+270) && ((z <= 1.7e+270) || (!(z <= 1.95e+276) && ((z <= 1.35e+283) || (!(z <= 2.8e+289) && (z <= 2.05e+295)))))))))))))))))))))))))))))))
		tmp = Float64(x * Float64(-z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -y;
	tmp = 0.0;
	if (z <= -34.0)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = x + y;
	elseif ((z <= 1850000.0) || (~((z <= 8e+36)) && ((z <= 1.05e+43) || (~((z <= 3.4e+59)) && ((z <= 1.2e+72) || (~((z <= 2.7e+85)) && ((z <= 3.2e+97) || (~((z <= 4.2e+99)) && ((z <= 6.8e+100) || (~((z <= 5.2e+117)) && ((z <= 2.2e+125) || (~((z <= 8.8e+126)) && ((z <= 4.5e+142) || (~((z <= 3.4e+150)) && ((z <= 2.55e+151) || (~((z <= 2.1e+156)) && ((z <= 5.7e+156) || (~((z <= 1.05e+173)) && ((z <= 4e+182) || (~((z <= 9.2e+184)) && ((z <= 2.4e+191) || (~((z <= 2.05e+211)) && ((z <= 4.2e+232) || (~((z <= 1.6e+241)) && ((z <= 2.25e+265) || (~((z <= 1e+270)) && ((z <= 1.7e+270) || (~((z <= 1.95e+276)) && ((z <= 1.35e+283) || (~((z <= 2.8e+289)) && (z <= 2.05e+295)))))))))))))))))))))))))))))))
		tmp = x * -z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[z, -34.0], t$95$0, If[LessEqual[z, 1.0], N[(x + y), $MachinePrecision], If[Or[LessEqual[z, 1850000.0], And[N[Not[LessEqual[z, 8e+36]], $MachinePrecision], Or[LessEqual[z, 1.05e+43], And[N[Not[LessEqual[z, 3.4e+59]], $MachinePrecision], Or[LessEqual[z, 1.2e+72], And[N[Not[LessEqual[z, 2.7e+85]], $MachinePrecision], Or[LessEqual[z, 3.2e+97], And[N[Not[LessEqual[z, 4.2e+99]], $MachinePrecision], Or[LessEqual[z, 6.8e+100], And[N[Not[LessEqual[z, 5.2e+117]], $MachinePrecision], Or[LessEqual[z, 2.2e+125], And[N[Not[LessEqual[z, 8.8e+126]], $MachinePrecision], Or[LessEqual[z, 4.5e+142], And[N[Not[LessEqual[z, 3.4e+150]], $MachinePrecision], Or[LessEqual[z, 2.55e+151], And[N[Not[LessEqual[z, 2.1e+156]], $MachinePrecision], Or[LessEqual[z, 5.7e+156], And[N[Not[LessEqual[z, 1.05e+173]], $MachinePrecision], Or[LessEqual[z, 4e+182], And[N[Not[LessEqual[z, 9.2e+184]], $MachinePrecision], Or[LessEqual[z, 2.4e+191], And[N[Not[LessEqual[z, 2.05e+211]], $MachinePrecision], Or[LessEqual[z, 4.2e+232], And[N[Not[LessEqual[z, 1.6e+241]], $MachinePrecision], Or[LessEqual[z, 2.25e+265], And[N[Not[LessEqual[z, 1e+270]], $MachinePrecision], Or[LessEqual[z, 1.7e+270], And[N[Not[LessEqual[z, 1.95e+276]], $MachinePrecision], Or[LessEqual[z, 1.35e+283], And[N[Not[LessEqual[z, 2.8e+289]], $MachinePrecision], LessEqual[z, 2.05e+295]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]], N[(x * (-z)), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -34 or 1.85e6 < z < 8.00000000000000034e36 or 1.05000000000000001e43 < z < 3.40000000000000006e59 or 1.20000000000000005e72 < z < 2.69999999999999983e85 or 3.20000000000000016e97 < z < 4.2000000000000002e99 or 6.79999999999999988e100 < z < 5.1999999999999999e117 or 2.19999999999999991e125 < z < 8.79999999999999994e126 or 4.4999999999999999e142 < z < 3.39999999999999983e150 or 2.54999999999999998e151 < z < 2.09999999999999981e156 or 5.69999999999999998e156 < z < 1.05e173 or 4.0000000000000003e182 < z < 9.1999999999999999e184 or 2.39999999999999986e191 < z < 2.0499999999999999e211 or 4.19999999999999982e232 < z < 1.60000000000000002e241 or 2.24999999999999993e265 < z < 1e270 or 1.70000000000000008e270 < z < 1.9500000000000001e276 or 1.34999999999999991e283 < z < 2.79999999999999991e289 or 2.04999999999999992e295 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.1%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(x + y\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 99.1%

         \[\leadsto \color{blue}{-z \cdot \left(x + y\right)} \]

      2. distribute-lft-neg-out 99.1%

         \[\leadsto \color{blue}{\left(-z\right) \cdot \left(x + y\right)} \]

      3. *-commutative 99.1%

         \[\leadsto \color{blue}{\left(x + y\right) \cdot \left(-z\right)} \]

      4. +-commutative 99.1%

         \[\leadsto \color{blue}{\left(y + x\right)} \cdot \left(-z\right) \]

   5. Simplified 99.1%

      \[\leadsto \color{blue}{\left(y + x\right) \cdot \left(-z\right)} \]

   6. Taylor expanded in y around inf 46.7%

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

      1. associate-*r* 46.7%

         \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot z} \]

      2. mul-1-neg 46.7%

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

   8. Simplified 46.7%

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

   if -34 < z < 1

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 98.4%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 98.4%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 98.4%

      \[\leadsto \color{blue}{y + x} \]

   if 1 < z < 1.85e6 or 8.00000000000000034e36 < z < 1.05000000000000001e43 or 3.40000000000000006e59 < z < 1.20000000000000005e72 or 2.69999999999999983e85 < z < 3.20000000000000016e97 or 4.2000000000000002e99 < z < 6.79999999999999988e100 or 5.1999999999999999e117 < z < 2.19999999999999991e125 or 8.79999999999999994e126 < z < 4.4999999999999999e142 or 3.39999999999999983e150 < z < 2.54999999999999998e151 or 2.09999999999999981e156 < z < 5.69999999999999998e156 or 1.05e173 < z < 4.0000000000000003e182 or 9.1999999999999999e184 < z < 2.39999999999999986e191 or 2.0499999999999999e211 < z < 4.19999999999999982e232 or 1.60000000000000002e241 < z < 2.24999999999999993e265 or 1e270 < z < 1.70000000000000008e270 or 1.9500000000000001e276 < z < 1.34999999999999991e283 or 2.79999999999999991e289 < z < 2.04999999999999992e295

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 96.8%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(x + y\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 96.8%

         \[\leadsto \color{blue}{-z \cdot \left(x + y\right)} \]

      2. distribute-lft-neg-out 96.8%

         \[\leadsto \color{blue}{\left(-z\right) \cdot \left(x + y\right)} \]

      3. *-commutative 96.8%

         \[\leadsto \color{blue}{\left(x + y\right) \cdot \left(-z\right)} \]

      4. +-commutative 96.8%

         \[\leadsto \color{blue}{\left(y + x\right)} \cdot \left(-z\right) \]

   5. Simplified 96.8%

      \[\leadsto \color{blue}{\left(y + x\right) \cdot \left(-z\right)} \]

   6. Taylor expanded in y around 0 44.6%

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

      1. associate-*r* 44.6%

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot z} \]

      2. mul-1-neg 44.6%

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

   8. Simplified 44.6%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -34:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1850000 \lor \neg \left(z \leq 8 \cdot 10^{+36}\right) \land \left(z \leq 1.05 \cdot 10^{+43} \lor \neg \left(z \leq 3.4 \cdot 10^{+59}\right) \land \left(z \leq 1.2 \cdot 10^{+72} \lor \neg \left(z \leq 2.7 \cdot 10^{+85}\right) \land \left(z \leq 3.2 \cdot 10^{+97} \lor \neg \left(z \leq 4.2 \cdot 10^{+99}\right) \land \left(z \leq 6.8 \cdot 10^{+100} \lor \neg \left(z \leq 5.2 \cdot 10^{+117}\right) \land \left(z \leq 2.2 \cdot 10^{+125} \lor \neg \left(z \leq 8.8 \cdot 10^{+126}\right) \land \left(z \leq 4.5 \cdot 10^{+142} \lor \neg \left(z \leq 3.4 \cdot 10^{+150}\right) \land \left(z \leq 2.55 \cdot 10^{+151} \lor \neg \left(z \leq 2.1 \cdot 10^{+156}\right) \land \left(z \leq 5.7 \cdot 10^{+156} \lor \neg \left(z \leq 1.05 \cdot 10^{+173}\right) \land \left(z \leq 4 \cdot 10^{+182} \lor \neg \left(z \leq 9.2 \cdot 10^{+184}\right) \land \left(z \leq 2.4 \cdot 10^{+191} \lor \neg \left(z \leq 2.05 \cdot 10^{+211}\right) \land \left(z \leq 4.2 \cdot 10^{+232} \lor \neg \left(z \leq 1.6 \cdot 10^{+241}\right) \land \left(z \leq 2.25 \cdot 10^{+265} \lor \neg \left(z \leq 10^{+270}\right) \land \left(z \leq 1.7 \cdot 10^{+270} \lor \neg \left(z \leq 1.95 \cdot 10^{+276}\right) \land \left(z \leq 1.35 \cdot 10^{+283} \lor \neg \left(z \leq 2.8 \cdot 10^{+289}\right) \land z \leq 2.05 \cdot 10^{+295}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.14 \cdot 10^{+21} \lor \neg \left(z \leq 1\right) \land \left(z \leq 5.9 \cdot 10^{+79} \lor \neg \left(z \leq 6 \cdot 10^{+79}\right) \land \left(z \leq 6.3 \cdot 10^{+149} \lor \neg \left(z \leq 6.5 \cdot 10^{+149}\right) \land \left(z \leq 1.12 \cdot 10^{+157} \lor \neg \left(z \leq 3 \cdot 10^{+167}\right) \land \left(z \leq 1.25 \cdot 10^{+184} \lor \neg \left(z \leq 1.28 \cdot 10^{+184}\right) \land \left(z \leq 6.5 \cdot 10^{+240} \lor \neg \left(z \leq 6.8 \cdot 10^{+240}\right) \land \left(z \leq 3.5 \cdot 10^{+283} \lor \neg \left(z \leq 3.1 \cdot 10^{+288}\right) \land z \leq 8.2 \cdot 10^{+297}\right)\right)\right)\right)\right)\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.14e+21)
         (and (not (<= z 1.0))
              (or (<= z 5.9e+79)
                  (and (not (<= z 6e+79))
                       (or (<= z 6.3e+149)
                           (and (not (<= z 6.5e+149))
                                (or (<= z 1.12e+157)
                                    (and (not (<= z 3e+167))
                                         (or (<= z 1.25e+184)
                                             (and (not (<= z 1.28e+184))
                                                  (or (<= z 6.5e+240)
                                                      (and (not
                                                            (<= z 6.8e+240))
                                                           (or (<= z 3.5e+283)
                                                               (and (not
                                                                     (<=
                                                                      z
                                                                      3.1e+288))
                                                                    (<=
                                                                     z
                                                                     8.2e+297)))))))))))))))
   (* x (- z))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.14e+21) || (!(z <= 1.0) && ((z <= 5.9e+79) || (!(z <= 6e+79) && ((z <= 6.3e+149) || (!(z <= 6.5e+149) && ((z <= 1.12e+157) || (!(z <= 3e+167) && ((z <= 1.25e+184) || (!(z <= 1.28e+184) && ((z <= 6.5e+240) || (!(z <= 6.8e+240) && ((z <= 3.5e+283) || (!(z <= 3.1e+288) && (z <= 8.2e+297))))))))))))))) {
		tmp = x * -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.14d+21)) .or. (.not. (z <= 1.0d0)) .and. (z <= 5.9d+79) .or. (.not. (z <= 6d+79)) .and. (z <= 6.3d+149) .or. (.not. (z <= 6.5d+149)) .and. (z <= 1.12d+157) .or. (.not. (z <= 3d+167)) .and. (z <= 1.25d+184) .or. (.not. (z <= 1.28d+184)) .and. (z <= 6.5d+240) .or. (.not. (z <= 6.8d+240)) .and. (z <= 3.5d+283) .or. (.not. (z <= 3.1d+288)) .and. (z <= 8.2d+297)) then
        tmp = x * -z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.14e+21) || (!(z <= 1.0) && ((z <= 5.9e+79) || (!(z <= 6e+79) && ((z <= 6.3e+149) || (!(z <= 6.5e+149) && ((z <= 1.12e+157) || (!(z <= 3e+167) && ((z <= 1.25e+184) || (!(z <= 1.28e+184) && ((z <= 6.5e+240) || (!(z <= 6.8e+240) && ((z <= 3.5e+283) || (!(z <= 3.1e+288) && (z <= 8.2e+297))))))))))))))) {
		tmp = x * -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.14e+21) or (not (z <= 1.0) and ((z <= 5.9e+79) or (not (z <= 6e+79) and ((z <= 6.3e+149) or (not (z <= 6.5e+149) and ((z <= 1.12e+157) or (not (z <= 3e+167) and ((z <= 1.25e+184) or (not (z <= 1.28e+184) and ((z <= 6.5e+240) or (not (z <= 6.8e+240) and ((z <= 3.5e+283) or (not (z <= 3.1e+288) and (z <= 8.2e+297)))))))))))))):
		tmp = x * -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.14e+21) || (!(z <= 1.0) && ((z <= 5.9e+79) || (!(z <= 6e+79) && ((z <= 6.3e+149) || (!(z <= 6.5e+149) && ((z <= 1.12e+157) || (!(z <= 3e+167) && ((z <= 1.25e+184) || (!(z <= 1.28e+184) && ((z <= 6.5e+240) || (!(z <= 6.8e+240) && ((z <= 3.5e+283) || (!(z <= 3.1e+288) && (z <= 8.2e+297)))))))))))))))
		tmp = Float64(x * Float64(-z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.14e+21) || (~((z <= 1.0)) && ((z <= 5.9e+79) || (~((z <= 6e+79)) && ((z <= 6.3e+149) || (~((z <= 6.5e+149)) && ((z <= 1.12e+157) || (~((z <= 3e+167)) && ((z <= 1.25e+184) || (~((z <= 1.28e+184)) && ((z <= 6.5e+240) || (~((z <= 6.8e+240)) && ((z <= 3.5e+283) || (~((z <= 3.1e+288)) && (z <= 8.2e+297)))))))))))))))
		tmp = x * -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.14e+21], And[N[Not[LessEqual[z, 1.0]], $MachinePrecision], Or[LessEqual[z, 5.9e+79], And[N[Not[LessEqual[z, 6e+79]], $MachinePrecision], Or[LessEqual[z, 6.3e+149], And[N[Not[LessEqual[z, 6.5e+149]], $MachinePrecision], Or[LessEqual[z, 1.12e+157], And[N[Not[LessEqual[z, 3e+167]], $MachinePrecision], Or[LessEqual[z, 1.25e+184], And[N[Not[LessEqual[z, 1.28e+184]], $MachinePrecision], Or[LessEqual[z, 6.5e+240], And[N[Not[LessEqual[z, 6.8e+240]], $MachinePrecision], Or[LessEqual[z, 3.5e+283], And[N[Not[LessEqual[z, 3.1e+288]], $MachinePrecision], LessEqual[z, 8.2e+297]]]]]]]]]]]]]]], N[(x * (-z)), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.14e21 or 1 < z < 5.9e79 or 5.99999999999999948e79 < z < 6.3e149 or 6.50000000000000015e149 < z < 1.11999999999999995e157 or 3.00000000000000012e167 < z < 1.25e184 or 1.2800000000000001e184 < z < 6.50000000000000018e240 or 6.80000000000000017e240 < z < 3.49999999999999995e283 or 3.1e288 < z < 8.2000000000000003e297

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 98.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(x + y\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 98.5%

         \[\leadsto \color{blue}{-z \cdot \left(x + y\right)} \]

      2. distribute-lft-neg-out 98.5%

         \[\leadsto \color{blue}{\left(-z\right) \cdot \left(x + y\right)} \]

      3. *-commutative 98.5%

         \[\leadsto \color{blue}{\left(x + y\right) \cdot \left(-z\right)} \]

      4. +-commutative 98.5%

         \[\leadsto \color{blue}{\left(y + x\right)} \cdot \left(-z\right) \]

   5. Simplified 98.5%

      \[\leadsto \color{blue}{\left(y + x\right) \cdot \left(-z\right)} \]

   6. Taylor expanded in y around 0 55.1%

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

      1. associate-*r* 55.1%

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot z} \]

      2. mul-1-neg 55.1%

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

   8. Simplified 55.1%

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

   if -1.14e21 < z < 1 or 5.9e79 < z < 5.99999999999999948e79 or 6.3e149 < z < 6.50000000000000015e149 or 1.11999999999999995e157 < z < 3.00000000000000012e167 or 1.25e184 < z < 1.2800000000000001e184 or 6.50000000000000018e240 < z < 6.80000000000000017e240 or 3.49999999999999995e283 < z < 3.1e288 or 8.2000000000000003e297 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 89.6%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 89.6%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 89.6%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.14 \cdot 10^{+21} \lor \neg \left(z \leq 1\right) \land \left(z \leq 5.9 \cdot 10^{+79} \lor \neg \left(z \leq 6 \cdot 10^{+79}\right) \land \left(z \leq 6.3 \cdot 10^{+149} \lor \neg \left(z \leq 6.5 \cdot 10^{+149}\right) \land \left(z \leq 1.12 \cdot 10^{+157} \lor \neg \left(z \leq 3 \cdot 10^{+167}\right) \land \left(z \leq 1.25 \cdot 10^{+184} \lor \neg \left(z \leq 1.28 \cdot 10^{+184}\right) \land \left(z \leq 6.5 \cdot 10^{+240} \lor \neg \left(z \leq 6.8 \cdot 10^{+240}\right) \land \left(z \leq 3.5 \cdot 10^{+283} \lor \neg \left(z \leq 3.1 \cdot 10^{+288}\right) \land z \leq 8.2 \cdot 10^{+297}\right)\right)\right)\right)\right)\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - z\right)\\ t_1 := z \cdot \left(\left(-y\right) - x\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-16}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-7}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1900000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+14}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 z))) (t_1 (* z (- (- y) x))))
   (if (<= z -1.0)
     t_1
     (if (<= z 3.5e-16)
       (+ x y)
       (if (<= z 1.75e-7)
         t_0
         (if (<= z 1900000.0) (* x (- 1.0 z)) (if (<= z 2.4e+14) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - z);
	double t_1 = z * (-y - x);
	double tmp;
	if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= 3.5e-16) {
		tmp = x + y;
	} else if (z <= 1.75e-7) {
		tmp = t_0;
	} else if (z <= 1900000.0) {
		tmp = x * (1.0 - z);
	} else if (z <= 2.4e+14) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y * (1.0d0 - z)
    t_1 = z * (-y - x)
    if (z <= (-1.0d0)) then
        tmp = t_1
    else if (z <= 3.5d-16) then
        tmp = x + y
    else if (z <= 1.75d-7) then
        tmp = t_0
    else if (z <= 1900000.0d0) then
        tmp = x * (1.0d0 - z)
    else if (z <= 2.4d+14) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (1.0 - z);
	double t_1 = z * (-y - x);
	double tmp;
	if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= 3.5e-16) {
		tmp = x + y;
	} else if (z <= 1.75e-7) {
		tmp = t_0;
	} else if (z <= 1900000.0) {
		tmp = x * (1.0 - z);
	} else if (z <= 2.4e+14) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (1.0 - z)
	t_1 = z * (-y - x)
	tmp = 0
	if z <= -1.0:
		tmp = t_1
	elif z <= 3.5e-16:
		tmp = x + y
	elif z <= 1.75e-7:
		tmp = t_0
	elif z <= 1900000.0:
		tmp = x * (1.0 - z)
	elif z <= 2.4e+14:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(1.0 - z))
	t_1 = Float64(z * Float64(Float64(-y) - x))
	tmp = 0.0
	if (z <= -1.0)
		tmp = t_1;
	elseif (z <= 3.5e-16)
		tmp = Float64(x + y);
	elseif (z <= 1.75e-7)
		tmp = t_0;
	elseif (z <= 1900000.0)
		tmp = Float64(x * Float64(1.0 - z));
	elseif (z <= 2.4e+14)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (1.0 - z);
	t_1 = z * (-y - x);
	tmp = 0.0;
	if (z <= -1.0)
		tmp = t_1;
	elseif (z <= 3.5e-16)
		tmp = x + y;
	elseif (z <= 1.75e-7)
		tmp = t_0;
	elseif (z <= 1900000.0)
		tmp = x * (1.0 - z);
	elseif (z <= 2.4e+14)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[((-y) - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$1, If[LessEqual[z, 3.5e-16], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.75e-7], t$95$0, If[LessEqual[z, 1900000.0], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+14], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1 or 2.4e14 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.9%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(x + y\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 99.9%

         \[\leadsto \color{blue}{-z \cdot \left(x + y\right)} \]

      2. distribute-lft-neg-out 99.9%

         \[\leadsto \color{blue}{\left(-z\right) \cdot \left(x + y\right)} \]

      3. *-commutative 99.9%

         \[\leadsto \color{blue}{\left(x + y\right) \cdot \left(-z\right)} \]

      4. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(y + x\right)} \cdot \left(-z\right) \]

   5. Simplified 99.9%

      \[\leadsto \color{blue}{\left(y + x\right) \cdot \left(-z\right)} \]

   if -1 < z < 3.50000000000000017e-16

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 99.1%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 99.1%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 99.1%

      \[\leadsto \color{blue}{y + x} \]

   if 3.50000000000000017e-16 < z < 1.74999999999999992e-7 or 1.9e6 < z < 2.4e14

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 3.0%

      \[\leadsto \color{blue}{y \cdot \left(1 - z\right)} \]

   if 1.74999999999999992e-7 < z < 1.9e6

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 50.8%

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

      1. *-commutative 50.8%

         \[\leadsto \color{blue}{\left(1 - z\right) \cdot x} \]

   5. Simplified 50.8%

      \[\leadsto \color{blue}{\left(1 - z\right) \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;z \cdot \left(\left(-y\right) - x\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-16}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 1900000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+14}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(-y\right) - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ x + y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x y))

C

double code(double x, double y, double z) {
	return x + y;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + y
end function

Java

public static double code(double x, double y, double z) {
	return x + y;
}

Python

def code(x, y, z):
	return x + y

Julia

function code(x, y, z)
	return Float64(x + y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + y;
end

Wolfram

code[x_, y_, z_] := N[(x + y), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]
2. Add Preprocessing

3. Taylor expanded in z around 0 47.2%

   \[\leadsto \color{blue}{x + y} \]
4. Step-by-step derivation

   1. +-commutative 47.2%

      \[\leadsto \color{blue}{y + x} \]

5. Simplified 47.2%

   \[\leadsto \color{blue}{y + x} \]

6. Final simplification 47.2%

   \[\leadsto x + y \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))