Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, J

Percentage Accurate: 95.9% → 95.7%

Time: 40.8s

Alternatives: 14

Speedup: 1.0×

• 33.1% of points produce a very large (infinite) output. You may want to add a precondition.

• could not determine a ground truth

  1. x = 1.4763878054994096e+47
  2. y = 5.23696654059091e+60
  3. z = -6.705385676835288e+230
  4. t = 5.863734107026751e+83
  5. a = -5.876776430880368e-28
  6. b = -2.386846991330748e+244
  7. c = -2.567534968792053e-95

Specification

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (fma x (* 9.0 y) (fma z (* t (* -4.0 a)) b)) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return fma(x, (9.0 * y), fma(z, (t * (-4.0 * a)), b)) / (z * c);
}

Julia

function code(x, y, z, t, a, b, c)
	return Float64(fma(x, Float64(9.0 * y), fma(z, Float64(t * Float64(-4.0 * a)), b)) / Float64(z * c))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(z * N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.7%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

3. Simplified 96.1%

   \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c}} \]

4. Final simplification 96.1%

   \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c} \]

Alternative 2: 53.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(t \cdot a\right)}{c}\\ t_2 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{if}\;x \leq -5 \cdot 10^{+117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.28 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-37}:\\ \;\;\;\;\frac{b \cdot \frac{1}{c}}{z}\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-29}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* -4.0 (* t a)) c)) (t_2 (* 9.0 (* (/ y c) (/ x z)))))
   (if (<= x -5e+117)
     t_2
     (if (<= x -1.28e+72)
       t_1
       (if (<= x -1.2e+53)
         t_2
         (if (<= x -1.55e-37)
           (/ (* b (/ 1.0 c)) z)
           (if (<= x -2.2e-131)
             t_1
             (if (<= x 1.2e-29) (* b (/ 1.0 (* z c))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (-4.0 * (t * a)) / c;
	double t_2 = 9.0 * ((y / c) * (x / z));
	double tmp;
	if (x <= -5e+117) {
		tmp = t_2;
	} else if (x <= -1.28e+72) {
		tmp = t_1;
	} else if (x <= -1.2e+53) {
		tmp = t_2;
	} else if (x <= -1.55e-37) {
		tmp = (b * (1.0 / c)) / z;
	} else if (x <= -2.2e-131) {
		tmp = t_1;
	} else if (x <= 1.2e-29) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((-4.0d0) * (t * a)) / c
    t_2 = 9.0d0 * ((y / c) * (x / z))
    if (x <= (-5d+117)) then
        tmp = t_2
    else if (x <= (-1.28d+72)) then
        tmp = t_1
    else if (x <= (-1.2d+53)) then
        tmp = t_2
    else if (x <= (-1.55d-37)) then
        tmp = (b * (1.0d0 / c)) / z
    else if (x <= (-2.2d-131)) then
        tmp = t_1
    else if (x <= 1.2d-29) then
        tmp = b * (1.0d0 / (z * c))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (-4.0 * (t * a)) / c;
	double t_2 = 9.0 * ((y / c) * (x / z));
	double tmp;
	if (x <= -5e+117) {
		tmp = t_2;
	} else if (x <= -1.28e+72) {
		tmp = t_1;
	} else if (x <= -1.2e+53) {
		tmp = t_2;
	} else if (x <= -1.55e-37) {
		tmp = (b * (1.0 / c)) / z;
	} else if (x <= -2.2e-131) {
		tmp = t_1;
	} else if (x <= 1.2e-29) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (-4.0 * (t * a)) / c
	t_2 = 9.0 * ((y / c) * (x / z))
	tmp = 0
	if x <= -5e+117:
		tmp = t_2
	elif x <= -1.28e+72:
		tmp = t_1
	elif x <= -1.2e+53:
		tmp = t_2
	elif x <= -1.55e-37:
		tmp = (b * (1.0 / c)) / z
	elif x <= -2.2e-131:
		tmp = t_1
	elif x <= 1.2e-29:
		tmp = b * (1.0 / (z * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(-4.0 * Float64(t * a)) / c)
	t_2 = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)))
	tmp = 0.0
	if (x <= -5e+117)
		tmp = t_2;
	elseif (x <= -1.28e+72)
		tmp = t_1;
	elseif (x <= -1.2e+53)
		tmp = t_2;
	elseif (x <= -1.55e-37)
		tmp = Float64(Float64(b * Float64(1.0 / c)) / z);
	elseif (x <= -2.2e-131)
		tmp = t_1;
	elseif (x <= 1.2e-29)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (-4.0 * (t * a)) / c;
	t_2 = 9.0 * ((y / c) * (x / z));
	tmp = 0.0;
	if (x <= -5e+117)
		tmp = t_2;
	elseif (x <= -1.28e+72)
		tmp = t_1;
	elseif (x <= -1.2e+53)
		tmp = t_2;
	elseif (x <= -1.55e-37)
		tmp = (b * (1.0 / c)) / z;
	elseif (x <= -2.2e-131)
		tmp = t_1;
	elseif (x <= 1.2e-29)
		tmp = b * (1.0 / (z * c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5e+117], t$95$2, If[LessEqual[x, -1.28e+72], t$95$1, If[LessEqual[x, -1.2e+53], t$95$2, If[LessEqual[x, -1.55e-37], N[(N[(b * N[(1.0 / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, -2.2e-131], t$95$1, If[LessEqual[x, 1.2e-29], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.99999999999999983e117 or -1.28000000000000009e72 < x < -1.2e53 or 1.19999999999999996e-29 < x

   1. Initial program 95.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

   3. Simplified 97.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c}} \]

   4. Taylor expanded in x around inf 69.5%

      \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z}} \]
   5. Step-by-step derivation

      1. times-frac 62.5%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{c} \cdot \frac{x}{z}\right)} \]

   6. Simplified 62.5%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)} \]

   if -4.99999999999999983e117 < x < -1.28000000000000009e72 or -1.54999999999999997e-37 < x < -2.2e-131

   1. Initial program 94.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 91.4%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in z around inf 51.4%

      \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right)}}{c} \]

   if -1.2e53 < x < -1.54999999999999997e-37

   1. Initial program 95.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 95.6%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 94.9%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in b around inf 51.4%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]
   5. Step-by-step derivation

      1. div-inv 51.4%

         \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]

   6. Applied egg-rr 51.4%

      \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]
   7. Step-by-step derivation

      1. associate-*l/ 51.3%

         \[\leadsto \color{blue}{\frac{b \cdot \frac{1}{c}}{z}} \]

   8. Applied egg-rr 51.3%

      \[\leadsto \color{blue}{\frac{b \cdot \frac{1}{c}}{z}} \]

   if -2.2e-131 < x < 1.19999999999999996e-29

   1. Initial program 94.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

   3. Simplified 94.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c}} \]

   4. Taylor expanded in b around inf 56.8%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 56.8%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 56.8%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   7. Step-by-step derivation

      1. div-inv 56.8%

         \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

   8. Applied egg-rr 56.8%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+117}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;x \leq -1.28 \cdot 10^{+72}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+53}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-37}:\\ \;\;\;\;\frac{b \cdot \frac{1}{c}}{z}\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-131}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-29}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \end{array} \]

Alternative 3: 54.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(t \cdot a\right)}{c}\\ t_2 := 9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.62 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+52}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-33}:\\ \;\;\;\;\frac{b \cdot \frac{1}{c}}{z}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-114}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* -4.0 (* t a)) c)) (t_2 (* 9.0 (/ (* x y) (* z c)))))
   (if (<= x -2.5e+117)
     t_2
     (if (<= x -1.62e+72)
       t_1
       (if (<= x -6.5e+52)
         (* 9.0 (* (/ y c) (/ x z)))
         (if (<= x -4.8e-33)
           (/ (* b (/ 1.0 c)) z)
           (if (<= x -3.5e-134)
             t_1
             (if (<= x 3.8e-114) (* b (/ 1.0 (* z c))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (-4.0 * (t * a)) / c;
	double t_2 = 9.0 * ((x * y) / (z * c));
	double tmp;
	if (x <= -2.5e+117) {
		tmp = t_2;
	} else if (x <= -1.62e+72) {
		tmp = t_1;
	} else if (x <= -6.5e+52) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (x <= -4.8e-33) {
		tmp = (b * (1.0 / c)) / z;
	} else if (x <= -3.5e-134) {
		tmp = t_1;
	} else if (x <= 3.8e-114) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((-4.0d0) * (t * a)) / c
    t_2 = 9.0d0 * ((x * y) / (z * c))
    if (x <= (-2.5d+117)) then
        tmp = t_2
    else if (x <= (-1.62d+72)) then
        tmp = t_1
    else if (x <= (-6.5d+52)) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    else if (x <= (-4.8d-33)) then
        tmp = (b * (1.0d0 / c)) / z
    else if (x <= (-3.5d-134)) then
        tmp = t_1
    else if (x <= 3.8d-114) then
        tmp = b * (1.0d0 / (z * c))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (-4.0 * (t * a)) / c;
	double t_2 = 9.0 * ((x * y) / (z * c));
	double tmp;
	if (x <= -2.5e+117) {
		tmp = t_2;
	} else if (x <= -1.62e+72) {
		tmp = t_1;
	} else if (x <= -6.5e+52) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (x <= -4.8e-33) {
		tmp = (b * (1.0 / c)) / z;
	} else if (x <= -3.5e-134) {
		tmp = t_1;
	} else if (x <= 3.8e-114) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (-4.0 * (t * a)) / c
	t_2 = 9.0 * ((x * y) / (z * c))
	tmp = 0
	if x <= -2.5e+117:
		tmp = t_2
	elif x <= -1.62e+72:
		tmp = t_1
	elif x <= -6.5e+52:
		tmp = 9.0 * ((y / c) * (x / z))
	elif x <= -4.8e-33:
		tmp = (b * (1.0 / c)) / z
	elif x <= -3.5e-134:
		tmp = t_1
	elif x <= 3.8e-114:
		tmp = b * (1.0 / (z * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(-4.0 * Float64(t * a)) / c)
	t_2 = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)))
	tmp = 0.0
	if (x <= -2.5e+117)
		tmp = t_2;
	elseif (x <= -1.62e+72)
		tmp = t_1;
	elseif (x <= -6.5e+52)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	elseif (x <= -4.8e-33)
		tmp = Float64(Float64(b * Float64(1.0 / c)) / z);
	elseif (x <= -3.5e-134)
		tmp = t_1;
	elseif (x <= 3.8e-114)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (-4.0 * (t * a)) / c;
	t_2 = 9.0 * ((x * y) / (z * c));
	tmp = 0.0;
	if (x <= -2.5e+117)
		tmp = t_2;
	elseif (x <= -1.62e+72)
		tmp = t_1;
	elseif (x <= -6.5e+52)
		tmp = 9.0 * ((y / c) * (x / z));
	elseif (x <= -4.8e-33)
		tmp = (b * (1.0 / c)) / z;
	elseif (x <= -3.5e-134)
		tmp = t_1;
	elseif (x <= 3.8e-114)
		tmp = b * (1.0 / (z * c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e+117], t$95$2, If[LessEqual[x, -1.62e+72], t$95$1, If[LessEqual[x, -6.5e+52], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.8e-33], N[(N[(b * N[(1.0 / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, -3.5e-134], t$95$1, If[LessEqual[x, 3.8e-114], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.49999999999999992e117 or 3.7999999999999998e-114 < x

   1. Initial program 95.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

   3. Simplified 97.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c}} \]

   4. Taylor expanded in x around inf 65.0%

      \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z}} \]

   if -2.49999999999999992e117 < x < -1.62000000000000008e72 or -4.8e-33 < x < -3.4999999999999998e-134

   1. Initial program 94.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 91.4%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in z around inf 51.4%

      \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right)}}{c} \]

   if -1.62000000000000008e72 < x < -6.49999999999999996e52

   1. Initial program 100.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c}} \]

   4. Taylor expanded in x around inf 66.7%

      \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z}} \]
   5. Step-by-step derivation

      1. times-frac 66.7%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{c} \cdot \frac{x}{z}\right)} \]

   6. Simplified 66.7%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)} \]

   if -6.49999999999999996e52 < x < -4.8e-33

   1. Initial program 95.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 95.6%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 94.9%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in b around inf 51.4%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]
   5. Step-by-step derivation

      1. div-inv 51.4%

         \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]

   6. Applied egg-rr 51.4%

      \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]
   7. Step-by-step derivation

      1. associate-*l/ 51.3%

         \[\leadsto \color{blue}{\frac{b \cdot \frac{1}{c}}{z}} \]

   8. Applied egg-rr 51.3%

      \[\leadsto \color{blue}{\frac{b \cdot \frac{1}{c}}{z}} \]

   if -3.4999999999999998e-134 < x < 3.7999999999999998e-114

   1. Initial program 92.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

   3. Simplified 93.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c}} \]

   4. Taylor expanded in b around inf 61.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 61.3%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 61.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   7. Step-by-step derivation

      1. div-inv 61.3%

         \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

   8. Applied egg-rr 61.3%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+117}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;x \leq -1.62 \cdot 10^{+72}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+52}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-33}:\\ \;\;\;\;\frac{b \cdot \frac{1}{c}}{z}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-134}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-114}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \end{array} \]

Alternative 4: 54.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(t \cdot a\right)}{c}\\ t_2 := \frac{9}{z} \cdot \frac{x \cdot y}{c}\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+117}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.7 \cdot 10^{-39}:\\ \;\;\;\;\frac{b \cdot \frac{1}{c}}{z}\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-114}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* -4.0 (* t a)) c)) (t_2 (* (/ 9.0 z) (/ (* x y) c))))
   (if (<= x -2.5e+117)
     (* 9.0 (/ (* x y) (* z c)))
     (if (<= x -1.55e+72)
       t_1
       (if (<= x -9.6e+52)
         t_2
         (if (<= x -5.7e-39)
           (/ (* b (/ 1.0 c)) z)
           (if (<= x -2.8e-131)
             t_1
             (if (<= x 3.8e-114) (* b (/ 1.0 (* z c))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (-4.0 * (t * a)) / c;
	double t_2 = (9.0 / z) * ((x * y) / c);
	double tmp;
	if (x <= -2.5e+117) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (x <= -1.55e+72) {
		tmp = t_1;
	} else if (x <= -9.6e+52) {
		tmp = t_2;
	} else if (x <= -5.7e-39) {
		tmp = (b * (1.0 / c)) / z;
	} else if (x <= -2.8e-131) {
		tmp = t_1;
	} else if (x <= 3.8e-114) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((-4.0d0) * (t * a)) / c
    t_2 = (9.0d0 / z) * ((x * y) / c)
    if (x <= (-2.5d+117)) then
        tmp = 9.0d0 * ((x * y) / (z * c))
    else if (x <= (-1.55d+72)) then
        tmp = t_1
    else if (x <= (-9.6d+52)) then
        tmp = t_2
    else if (x <= (-5.7d-39)) then
        tmp = (b * (1.0d0 / c)) / z
    else if (x <= (-2.8d-131)) then
        tmp = t_1
    else if (x <= 3.8d-114) then
        tmp = b * (1.0d0 / (z * c))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (-4.0 * (t * a)) / c;
	double t_2 = (9.0 / z) * ((x * y) / c);
	double tmp;
	if (x <= -2.5e+117) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (x <= -1.55e+72) {
		tmp = t_1;
	} else if (x <= -9.6e+52) {
		tmp = t_2;
	} else if (x <= -5.7e-39) {
		tmp = (b * (1.0 / c)) / z;
	} else if (x <= -2.8e-131) {
		tmp = t_1;
	} else if (x <= 3.8e-114) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (-4.0 * (t * a)) / c
	t_2 = (9.0 / z) * ((x * y) / c)
	tmp = 0
	if x <= -2.5e+117:
		tmp = 9.0 * ((x * y) / (z * c))
	elif x <= -1.55e+72:
		tmp = t_1
	elif x <= -9.6e+52:
		tmp = t_2
	elif x <= -5.7e-39:
		tmp = (b * (1.0 / c)) / z
	elif x <= -2.8e-131:
		tmp = t_1
	elif x <= 3.8e-114:
		tmp = b * (1.0 / (z * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(-4.0 * Float64(t * a)) / c)
	t_2 = Float64(Float64(9.0 / z) * Float64(Float64(x * y) / c))
	tmp = 0.0
	if (x <= -2.5e+117)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)));
	elseif (x <= -1.55e+72)
		tmp = t_1;
	elseif (x <= -9.6e+52)
		tmp = t_2;
	elseif (x <= -5.7e-39)
		tmp = Float64(Float64(b * Float64(1.0 / c)) / z);
	elseif (x <= -2.8e-131)
		tmp = t_1;
	elseif (x <= 3.8e-114)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (-4.0 * (t * a)) / c;
	t_2 = (9.0 / z) * ((x * y) / c);
	tmp = 0.0;
	if (x <= -2.5e+117)
		tmp = 9.0 * ((x * y) / (z * c));
	elseif (x <= -1.55e+72)
		tmp = t_1;
	elseif (x <= -9.6e+52)
		tmp = t_2;
	elseif (x <= -5.7e-39)
		tmp = (b * (1.0 / c)) / z;
	elseif (x <= -2.8e-131)
		tmp = t_1;
	elseif (x <= 3.8e-114)
		tmp = b * (1.0 / (z * c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, Block[{t$95$2 = N[(N[(9.0 / z), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e+117], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.55e+72], t$95$1, If[LessEqual[x, -9.6e+52], t$95$2, If[LessEqual[x, -5.7e-39], N[(N[(b * N[(1.0 / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, -2.8e-131], t$95$1, If[LessEqual[x, 3.8e-114], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.49999999999999992e117

   1. Initial program 91.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

   3. Simplified 97.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c}} \]

   4. Taylor expanded in x around inf 73.9%

      \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z}} \]

   if -2.49999999999999992e117 < x < -1.54999999999999994e72 or -5.6999999999999997e-39 < x < -2.8e-131

   1. Initial program 94.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 91.4%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in z around inf 51.4%

      \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right)}}{c} \]

   if -1.54999999999999994e72 < x < -9.5999999999999999e52 or 3.7999999999999998e-114 < x

   1. Initial program 98.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 92.7%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in t around 0 68.4%

      \[\leadsto \frac{\color{blue}{\frac{b}{z} + 9 \cdot \frac{y \cdot x}{z}}}{c} \]

   5. Taylor expanded in z around -inf 78.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{-9 \cdot \left(y \cdot x\right) + -1 \cdot b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 78.3%

         \[\leadsto \color{blue}{-\frac{-9 \cdot \left(y \cdot x\right) + -1 \cdot b}{c \cdot z}} \]

      2. distribute-neg-frac 78.3%

         \[\leadsto \color{blue}{\frac{-\left(-9 \cdot \left(y \cdot x\right) + -1 \cdot b\right)}{c \cdot z}} \]

      3. neg-mul-1 78.3%

         \[\leadsto \frac{-\left(-9 \cdot \left(y \cdot x\right) + \color{blue}{\left(-b\right)}\right)}{c \cdot z} \]

      4. unsub-neg 78.3%

         \[\leadsto \frac{-\color{blue}{\left(-9 \cdot \left(y \cdot x\right) - b\right)}}{c \cdot z} \]

      5. *-commutative 78.3%

         \[\leadsto \frac{-\left(\color{blue}{\left(y \cdot x\right) \cdot -9} - b\right)}{c \cdot z} \]

      6. associate-*l* 78.2%

         \[\leadsto \frac{-\left(\color{blue}{y \cdot \left(x \cdot -9\right)} - b\right)}{c \cdot z} \]

      7. *-commutative 78.2%

         \[\leadsto \frac{-\left(y \cdot \left(x \cdot -9\right) - b\right)}{\color{blue}{z \cdot c}} \]

   7. Simplified 78.2%

      \[\leadsto \color{blue}{\frac{-\left(y \cdot \left(x \cdot -9\right) - b\right)}{z \cdot c}} \]

   8. Taylor expanded in y around inf 59.6%

      \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 59.6%

         \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{c \cdot z}} \]

      2. *-commutative 59.6%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{\color{blue}{z \cdot c}} \]

      3. times-frac 56.0%

         \[\leadsto \color{blue}{\frac{9}{z} \cdot \frac{y \cdot x}{c}} \]

   10. Simplified 56.0%

       \[\leadsto \color{blue}{\frac{9}{z} \cdot \frac{y \cdot x}{c}} \]

   if -9.5999999999999999e52 < x < -5.6999999999999997e-39

   1. Initial program 95.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 95.6%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 94.9%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in b around inf 51.4%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]
   5. Step-by-step derivation

      1. div-inv 51.4%

         \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]

   6. Applied egg-rr 51.4%

      \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]
   7. Step-by-step derivation

      1. associate-*l/ 51.3%

         \[\leadsto \color{blue}{\frac{b \cdot \frac{1}{c}}{z}} \]

   8. Applied egg-rr 51.3%

      \[\leadsto \color{blue}{\frac{b \cdot \frac{1}{c}}{z}} \]

   if -2.8e-131 < x < 3.7999999999999998e-114

   1. Initial program 92.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

   3. Simplified 93.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c}} \]

   4. Taylor expanded in b around inf 61.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 61.3%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 61.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   7. Step-by-step derivation

      1. div-inv 61.3%

         \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

   8. Applied egg-rr 61.3%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+117}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+72}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{+52}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{x \cdot y}{c}\\ \mathbf{elif}\;x \leq -5.7 \cdot 10^{-39}:\\ \;\;\;\;\frac{b \cdot \frac{1}{c}}{z}\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-131}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-114}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{x \cdot y}{c}\\ \end{array} \]

Alternative 5: 54.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+117}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.1 \cdot 10^{+52}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 9\right)}{z \cdot c}\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-38}:\\ \;\;\;\;\frac{b \cdot \frac{1}{c}}{z}\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-114}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{x \cdot y}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* -4.0 (* t a)) c)))
   (if (<= x -2.5e+117)
     (* 9.0 (/ (* x y) (* z c)))
     (if (<= x -1.55e+72)
       t_1
       (if (<= x -8.1e+52)
         (/ (* y (* x 9.0)) (* z c))
         (if (<= x -2.8e-38)
           (/ (* b (/ 1.0 c)) z)
           (if (<= x -9.6e-132)
             t_1
             (if (<= x 3.2e-114)
               (* b (/ 1.0 (* z c)))
               (* (/ 9.0 z) (/ (* x y) c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (-4.0 * (t * a)) / c;
	double tmp;
	if (x <= -2.5e+117) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (x <= -1.55e+72) {
		tmp = t_1;
	} else if (x <= -8.1e+52) {
		tmp = (y * (x * 9.0)) / (z * c);
	} else if (x <= -2.8e-38) {
		tmp = (b * (1.0 / c)) / z;
	} else if (x <= -9.6e-132) {
		tmp = t_1;
	} else if (x <= 3.2e-114) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = (9.0 / z) * ((x * y) / c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((-4.0d0) * (t * a)) / c
    if (x <= (-2.5d+117)) then
        tmp = 9.0d0 * ((x * y) / (z * c))
    else if (x <= (-1.55d+72)) then
        tmp = t_1
    else if (x <= (-8.1d+52)) then
        tmp = (y * (x * 9.0d0)) / (z * c)
    else if (x <= (-2.8d-38)) then
        tmp = (b * (1.0d0 / c)) / z
    else if (x <= (-9.6d-132)) then
        tmp = t_1
    else if (x <= 3.2d-114) then
        tmp = b * (1.0d0 / (z * c))
    else
        tmp = (9.0d0 / z) * ((x * y) / c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (-4.0 * (t * a)) / c;
	double tmp;
	if (x <= -2.5e+117) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (x <= -1.55e+72) {
		tmp = t_1;
	} else if (x <= -8.1e+52) {
		tmp = (y * (x * 9.0)) / (z * c);
	} else if (x <= -2.8e-38) {
		tmp = (b * (1.0 / c)) / z;
	} else if (x <= -9.6e-132) {
		tmp = t_1;
	} else if (x <= 3.2e-114) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = (9.0 / z) * ((x * y) / c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (-4.0 * (t * a)) / c
	tmp = 0
	if x <= -2.5e+117:
		tmp = 9.0 * ((x * y) / (z * c))
	elif x <= -1.55e+72:
		tmp = t_1
	elif x <= -8.1e+52:
		tmp = (y * (x * 9.0)) / (z * c)
	elif x <= -2.8e-38:
		tmp = (b * (1.0 / c)) / z
	elif x <= -9.6e-132:
		tmp = t_1
	elif x <= 3.2e-114:
		tmp = b * (1.0 / (z * c))
	else:
		tmp = (9.0 / z) * ((x * y) / c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(-4.0 * Float64(t * a)) / c)
	tmp = 0.0
	if (x <= -2.5e+117)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)));
	elseif (x <= -1.55e+72)
		tmp = t_1;
	elseif (x <= -8.1e+52)
		tmp = Float64(Float64(y * Float64(x * 9.0)) / Float64(z * c));
	elseif (x <= -2.8e-38)
		tmp = Float64(Float64(b * Float64(1.0 / c)) / z);
	elseif (x <= -9.6e-132)
		tmp = t_1;
	elseif (x <= 3.2e-114)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	else
		tmp = Float64(Float64(9.0 / z) * Float64(Float64(x * y) / c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (-4.0 * (t * a)) / c;
	tmp = 0.0;
	if (x <= -2.5e+117)
		tmp = 9.0 * ((x * y) / (z * c));
	elseif (x <= -1.55e+72)
		tmp = t_1;
	elseif (x <= -8.1e+52)
		tmp = (y * (x * 9.0)) / (z * c);
	elseif (x <= -2.8e-38)
		tmp = (b * (1.0 / c)) / z;
	elseif (x <= -9.6e-132)
		tmp = t_1;
	elseif (x <= 3.2e-114)
		tmp = b * (1.0 / (z * c));
	else
		tmp = (9.0 / z) * ((x * y) / c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[x, -2.5e+117], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.55e+72], t$95$1, If[LessEqual[x, -8.1e+52], N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.8e-38], N[(N[(b * N[(1.0 / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, -9.6e-132], t$95$1, If[LessEqual[x, 3.2e-114], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(9.0 / z), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -2.49999999999999992e117

   1. Initial program 91.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

   3. Simplified 97.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c}} \]

   4. Taylor expanded in x around inf 73.9%

      \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z}} \]

   if -2.49999999999999992e117 < x < -1.54999999999999994e72 or -2.8e-38 < x < -9.60000000000000062e-132

   1. Initial program 94.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 91.4%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in z around inf 51.4%

      \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right)}}{c} \]

   if -1.54999999999999994e72 < x < -8.09999999999999995e52

   1. Initial program 100.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c}} \]

   4. Taylor expanded in x around inf 66.7%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} \]
   5. Step-by-step derivation

      1. expm1-log1p-u 32.1%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(9 \cdot \left(y \cdot x\right)\right)\right)}}{z \cdot c} \]

      2. expm1-udef 32.3%

         \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(9 \cdot \left(y \cdot x\right)\right)} - 1}}{z \cdot c} \]

   6. Applied egg-rr 32.3%

      \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(9 \cdot \left(y \cdot x\right)\right)} - 1}}{z \cdot c} \]
   7. Step-by-step derivation

      1. expm1-def 32.1%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(9 \cdot \left(y \cdot x\right)\right)\right)}}{z \cdot c} \]

      2. expm1-log1p 66.7%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} \]

      3. *-commutative 66.7%

         \[\leadsto \frac{9 \cdot \color{blue}{\left(x \cdot y\right)}}{z \cdot c} \]

      4. associate-*r* 67.0%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y}}{z \cdot c} \]

   8. Simplified 67.0%

      \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y}}{z \cdot c} \]

   if -8.09999999999999995e52 < x < -2.8e-38

   1. Initial program 95.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 95.6%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 94.9%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in b around inf 51.4%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]
   5. Step-by-step derivation

      1. div-inv 51.4%

         \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]

   6. Applied egg-rr 51.4%

      \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]
   7. Step-by-step derivation

      1. associate-*l/ 51.3%

         \[\leadsto \color{blue}{\frac{b \cdot \frac{1}{c}}{z}} \]

   8. Applied egg-rr 51.3%

      \[\leadsto \color{blue}{\frac{b \cdot \frac{1}{c}}{z}} \]

   if -9.60000000000000062e-132 < x < 3.2000000000000002e-114

   1. Initial program 92.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

   3. Simplified 93.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c}} \]

   4. Taylor expanded in b around inf 61.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 61.3%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 61.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   7. Step-by-step derivation

      1. div-inv 61.3%

         \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

   8. Applied egg-rr 61.3%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

   if 3.2000000000000002e-114 < x

   1. Initial program 98.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 93.4%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 92.0%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in t around 0 69.9%

      \[\leadsto \frac{\color{blue}{\frac{b}{z} + 9 \cdot \frac{y \cdot x}{z}}}{c} \]

   5. Taylor expanded in z around -inf 79.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{-9 \cdot \left(y \cdot x\right) + -1 \cdot b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 79.2%

         \[\leadsto \color{blue}{-\frac{-9 \cdot \left(y \cdot x\right) + -1 \cdot b}{c \cdot z}} \]

      2. distribute-neg-frac 79.2%

         \[\leadsto \color{blue}{\frac{-\left(-9 \cdot \left(y \cdot x\right) + -1 \cdot b\right)}{c \cdot z}} \]

      3. neg-mul-1 79.2%

         \[\leadsto \frac{-\left(-9 \cdot \left(y \cdot x\right) + \color{blue}{\left(-b\right)}\right)}{c \cdot z} \]

      4. unsub-neg 79.2%

         \[\leadsto \frac{-\color{blue}{\left(-9 \cdot \left(y \cdot x\right) - b\right)}}{c \cdot z} \]

      5. *-commutative 79.2%

         \[\leadsto \frac{-\left(\color{blue}{\left(y \cdot x\right) \cdot -9} - b\right)}{c \cdot z} \]

      6. associate-*l* 79.1%

         \[\leadsto \frac{-\left(\color{blue}{y \cdot \left(x \cdot -9\right)} - b\right)}{c \cdot z} \]

      7. *-commutative 79.1%

         \[\leadsto \frac{-\left(y \cdot \left(x \cdot -9\right) - b\right)}{\color{blue}{z \cdot c}} \]

   7. Simplified 79.1%

      \[\leadsto \color{blue}{\frac{-\left(y \cdot \left(x \cdot -9\right) - b\right)}{z \cdot c}} \]

   8. Taylor expanded in y around inf 59.0%

      \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 59.1%

         \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{c \cdot z}} \]

      2. *-commutative 59.1%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{\color{blue}{z \cdot c}} \]

      3. times-frac 55.1%

         \[\leadsto \color{blue}{\frac{9}{z} \cdot \frac{y \cdot x}{c}} \]

   10. Simplified 55.1%

       \[\leadsto \color{blue}{\frac{9}{z} \cdot \frac{y \cdot x}{c}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+117}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+72}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;x \leq -8.1 \cdot 10^{+52}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 9\right)}{z \cdot c}\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-38}:\\ \;\;\;\;\frac{b \cdot \frac{1}{c}}{z}\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{-132}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-114}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{x \cdot y}{c}\\ \end{array} \]

Alternative 6: 83.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{-54}:\\ \;\;\;\;\frac{b - x \cdot \left(y \cdot -9\right)}{z \cdot c}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-30}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - y \cdot \left(x \cdot -9\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -2.25e-54)
   (/ (- b (* x (* y -9.0))) (* z c))
   (if (<= b 2e-30)
     (/ (- (* 9.0 (* x y)) (* 4.0 (* a (* z t)))) (* z c))
     (/ (- b (* y (* x -9.0))) (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.25e-54) {
		tmp = (b - (x * (y * -9.0))) / (z * c);
	} else if (b <= 2e-30) {
		tmp = ((9.0 * (x * y)) - (4.0 * (a * (z * t)))) / (z * c);
	} else {
		tmp = (b - (y * (x * -9.0))) / (z * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-2.25d-54)) then
        tmp = (b - (x * (y * (-9.0d0)))) / (z * c)
    else if (b <= 2d-30) then
        tmp = ((9.0d0 * (x * y)) - (4.0d0 * (a * (z * t)))) / (z * c)
    else
        tmp = (b - (y * (x * (-9.0d0)))) / (z * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.25e-54) {
		tmp = (b - (x * (y * -9.0))) / (z * c);
	} else if (b <= 2e-30) {
		tmp = ((9.0 * (x * y)) - (4.0 * (a * (z * t)))) / (z * c);
	} else {
		tmp = (b - (y * (x * -9.0))) / (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -2.25e-54:
		tmp = (b - (x * (y * -9.0))) / (z * c)
	elif b <= 2e-30:
		tmp = ((9.0 * (x * y)) - (4.0 * (a * (z * t)))) / (z * c)
	else:
		tmp = (b - (y * (x * -9.0))) / (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -2.25e-54)
		tmp = Float64(Float64(b - Float64(x * Float64(y * -9.0))) / Float64(z * c));
	elseif (b <= 2e-30)
		tmp = Float64(Float64(Float64(9.0 * Float64(x * y)) - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(z * c));
	else
		tmp = Float64(Float64(b - Float64(y * Float64(x * -9.0))) / Float64(z * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -2.25e-54)
		tmp = (b - (x * (y * -9.0))) / (z * c);
	elseif (b <= 2e-30)
		tmp = ((9.0 * (x * y)) - (4.0 * (a * (z * t)))) / (z * c);
	else
		tmp = (b - (y * (x * -9.0))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -2.25e-54], N[(N[(b - N[(x * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e-30], N[(N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(b - N[(y * N[(x * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.2499999999999999e-54

   1. Initial program 95.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 88.9%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.6%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in t around 0 79.4%

      \[\leadsto \frac{\color{blue}{\frac{b}{z} + 9 \cdot \frac{y \cdot x}{z}}}{c} \]

   5. Taylor expanded in z around -inf 91.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{-9 \cdot \left(y \cdot x\right) + -1 \cdot b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 91.2%

         \[\leadsto \color{blue}{-\frac{-9 \cdot \left(y \cdot x\right) + -1 \cdot b}{c \cdot z}} \]

      2. distribute-neg-frac 91.2%

         \[\leadsto \color{blue}{\frac{-\left(-9 \cdot \left(y \cdot x\right) + -1 \cdot b\right)}{c \cdot z}} \]

      3. neg-mul-1 91.2%

         \[\leadsto \frac{-\left(-9 \cdot \left(y \cdot x\right) + \color{blue}{\left(-b\right)}\right)}{c \cdot z} \]

      4. unsub-neg 91.2%

         \[\leadsto \frac{-\color{blue}{\left(-9 \cdot \left(y \cdot x\right) - b\right)}}{c \cdot z} \]

      5. *-commutative 91.2%

         \[\leadsto \frac{-\left(\color{blue}{\left(y \cdot x\right) \cdot -9} - b\right)}{c \cdot z} \]

      6. associate-*l* 91.2%

         \[\leadsto \frac{-\left(\color{blue}{y \cdot \left(x \cdot -9\right)} - b\right)}{c \cdot z} \]

      7. *-commutative 91.2%

         \[\leadsto \frac{-\left(y \cdot \left(x \cdot -9\right) - b\right)}{\color{blue}{z \cdot c}} \]

   7. Simplified 91.2%

      \[\leadsto \color{blue}{\frac{-\left(y \cdot \left(x \cdot -9\right) - b\right)}{z \cdot c}} \]

   8. Taylor expanded in z around 0 91.2%

      \[\leadsto \color{blue}{\frac{b - -9 \cdot \left(y \cdot x\right)}{c \cdot z}} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 69.9%

         \[\leadsto \frac{b - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-9 \cdot \left(y \cdot x\right)\right)\right)}}{c \cdot z} \]

      2. expm1-udef 69.5%

         \[\leadsto \frac{b - \color{blue}{\left(e^{\mathsf{log1p}\left(-9 \cdot \left(y \cdot x\right)\right)} - 1\right)}}{c \cdot z} \]

   10. Applied egg-rr 69.5%

       \[\leadsto \frac{b - \color{blue}{\left(e^{\mathsf{log1p}\left(-9 \cdot \left(y \cdot x\right)\right)} - 1\right)}}{c \cdot z} \]
   11. Step-by-step derivation

       1. expm1-def 69.9%

          \[\leadsto \frac{b - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-9 \cdot \left(y \cdot x\right)\right)\right)}}{c \cdot z} \]

       2. expm1-log1p 91.2%

          \[\leadsto \frac{b - \color{blue}{-9 \cdot \left(y \cdot x\right)}}{c \cdot z} \]

       3. *-commutative 91.2%

          \[\leadsto \frac{b - \color{blue}{\left(y \cdot x\right) \cdot -9}}{c \cdot z} \]

       4. *-commutative 91.2%

          \[\leadsto \frac{b - \color{blue}{\left(x \cdot y\right)} \cdot -9}{c \cdot z} \]

       5. associate-*l* 91.2%

          \[\leadsto \frac{b - \color{blue}{x \cdot \left(y \cdot -9\right)}}{c \cdot z} \]

   12. Simplified 91.2%

       \[\leadsto \frac{b - \color{blue}{x \cdot \left(y \cdot -9\right)}}{c \cdot z} \]

   if -2.2499999999999999e-54 < b < 2e-30

   1. Initial program 92.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-*l* 92.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      2. associate-*l* 93.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 93.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around 0 82.7%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}} \]

   if 2e-30 < b

   1. Initial program 96.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 88.8%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.7%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in t around 0 74.5%

      \[\leadsto \frac{\color{blue}{\frac{b}{z} + 9 \cdot \frac{y \cdot x}{z}}}{c} \]

   5. Taylor expanded in z around -inf 85.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{-9 \cdot \left(y \cdot x\right) + -1 \cdot b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 85.1%

         \[\leadsto \color{blue}{-\frac{-9 \cdot \left(y \cdot x\right) + -1 \cdot b}{c \cdot z}} \]

      2. distribute-neg-frac 85.1%

         \[\leadsto \color{blue}{\frac{-\left(-9 \cdot \left(y \cdot x\right) + -1 \cdot b\right)}{c \cdot z}} \]

      3. neg-mul-1 85.1%

         \[\leadsto \frac{-\left(-9 \cdot \left(y \cdot x\right) + \color{blue}{\left(-b\right)}\right)}{c \cdot z} \]

      4. unsub-neg 85.1%

         \[\leadsto \frac{-\color{blue}{\left(-9 \cdot \left(y \cdot x\right) - b\right)}}{c \cdot z} \]

      5. *-commutative 85.1%

         \[\leadsto \frac{-\left(\color{blue}{\left(y \cdot x\right) \cdot -9} - b\right)}{c \cdot z} \]

      6. associate-*l* 85.1%

         \[\leadsto \frac{-\left(\color{blue}{y \cdot \left(x \cdot -9\right)} - b\right)}{c \cdot z} \]

      7. *-commutative 85.1%

         \[\leadsto \frac{-\left(y \cdot \left(x \cdot -9\right) - b\right)}{\color{blue}{z \cdot c}} \]

   7. Simplified 85.1%

      \[\leadsto \color{blue}{\frac{-\left(y \cdot \left(x \cdot -9\right) - b\right)}{z \cdot c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{-54}:\\ \;\;\;\;\frac{b - x \cdot \left(y \cdot -9\right)}{z \cdot c}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-30}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - y \cdot \left(x \cdot -9\right)}{z \cdot c}\\ \end{array} \]

Alternative 7: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ t_2 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+235}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (* 9.0 (* x y))) (* z c))) (t_2 (* -4.0 (/ a (/ c t)))))
   (if (<= t -4.4e+235)
     t_2
     (if (<= t -5e+203)
       t_1
       (if (<= t -4.5e+151)
         t_2
         (if (<= t 1.25e+52) t_1 (* -4.0 (* t (/ a c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (9.0 * (x * y))) / (z * c);
	double t_2 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -4.4e+235) {
		tmp = t_2;
	} else if (t <= -5e+203) {
		tmp = t_1;
	} else if (t <= -4.5e+151) {
		tmp = t_2;
	} else if (t <= 1.25e+52) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b + (9.0d0 * (x * y))) / (z * c)
    t_2 = (-4.0d0) * (a / (c / t))
    if (t <= (-4.4d+235)) then
        tmp = t_2
    else if (t <= (-5d+203)) then
        tmp = t_1
    else if (t <= (-4.5d+151)) then
        tmp = t_2
    else if (t <= 1.25d+52) then
        tmp = t_1
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (9.0 * (x * y))) / (z * c);
	double t_2 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -4.4e+235) {
		tmp = t_2;
	} else if (t <= -5e+203) {
		tmp = t_1;
	} else if (t <= -4.5e+151) {
		tmp = t_2;
	} else if (t <= 1.25e+52) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b + (9.0 * (x * y))) / (z * c)
	t_2 = -4.0 * (a / (c / t))
	tmp = 0
	if t <= -4.4e+235:
		tmp = t_2
	elif t <= -5e+203:
		tmp = t_1
	elif t <= -4.5e+151:
		tmp = t_2
	elif t <= 1.25e+52:
		tmp = t_1
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c))
	t_2 = Float64(-4.0 * Float64(a / Float64(c / t)))
	tmp = 0.0
	if (t <= -4.4e+235)
		tmp = t_2;
	elseif (t <= -5e+203)
		tmp = t_1;
	elseif (t <= -4.5e+151)
		tmp = t_2;
	elseif (t <= 1.25e+52)
		tmp = t_1;
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + (9.0 * (x * y))) / (z * c);
	t_2 = -4.0 * (a / (c / t));
	tmp = 0.0;
	if (t <= -4.4e+235)
		tmp = t_2;
	elseif (t <= -5e+203)
		tmp = t_1;
	elseif (t <= -4.5e+151)
		tmp = t_2;
	elseif (t <= 1.25e+52)
		tmp = t_1;
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.4e+235], t$95$2, If[LessEqual[t, -5e+203], t$95$1, If[LessEqual[t, -4.5e+151], t$95$2, If[LessEqual[t, 1.25e+52], t$95$1, N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.4e235 or -4.99999999999999994e203 < t < -4.4999999999999999e151

   1. Initial program 84.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

   3. Simplified 89.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c}} \]

   4. Taylor expanded in z around inf 69.2%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. associate-/l* 85.8%

         \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

   6. Simplified 85.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a}{\frac{c}{t}}} \]

   if -4.4e235 < t < -4.99999999999999994e203 or -4.4999999999999999e151 < t < 1.25e52

   1. Initial program 97.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

   3. Simplified 97.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c}} \]

   4. Taylor expanded in z around 0 83.8%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right) + b}}{z \cdot c} \]

   if 1.25e52 < t

   1. Initial program 89.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

   3. Simplified 95.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c}} \]

   4. Taylor expanded in z around inf 48.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. associate-/l* 50.4%

         \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

      2. associate-/r/ 50.2%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

   6. Simplified 50.2%

      \[\leadsto \color{blue}{-4 \cdot \left(\frac{a}{c} \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+235}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+203}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+151}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+52}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 8: 95.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (b + ((x * (9.0d0 * y)) - ((z * 4.0d0) * (t * a)))) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.7%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-*l* 94.7%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. associate-*l* 95.4%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 95.4%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

4. Final simplification 95.4%

   \[\leadsto \frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c} \]

Alternative 9: 95.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.7%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

2. Final simplification 94.7%

   \[\leadsto \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \]

Alternative 10: 80.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0026 \lor \neg \left(z \leq 4.2 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -0.0026) (not (<= z 4.2e+61)))
   (/ (+ (/ b z) (* -4.0 (* t a))) c)
   (/ (+ b (* 9.0 (* x y))) (* z c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -0.0026) || !(z <= 4.2e+61)) {
		tmp = ((b / z) + (-4.0 * (t * a))) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-0.0026d0)) .or. (.not. (z <= 4.2d+61))) then
        tmp = ((b / z) + ((-4.0d0) * (t * a))) / c
    else
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -0.0026) || !(z <= 4.2e+61)) {
		tmp = ((b / z) + (-4.0 * (t * a))) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -0.0026) or not (z <= 4.2e+61):
		tmp = ((b / z) + (-4.0 * (t * a))) / c
	else:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -0.0026) || !(z <= 4.2e+61))
		tmp = Float64(Float64(Float64(b / z) + Float64(-4.0 * Float64(t * a))) / c);
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -0.0026) || ~((z <= 4.2e+61)))
		tmp = ((b / z) + (-4.0 * (t * a))) / c;
	else
		tmp = (b + (9.0 * (x * y))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -0.0026], N[Not[LessEqual[z, 4.2e+61]], $MachinePrecision]], N[(N[(N[(b / z), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0025999999999999999 or 4.2000000000000002e61 < z

   1. Initial program 88.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 87.2%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 94.1%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in x around 0 81.1%

      \[\leadsto \frac{\color{blue}{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}}{c} \]

   if -0.0025999999999999999 < z < 4.2000000000000002e61

   1. Initial program 96.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

   3. Simplified 95.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c}} \]

   4. Taylor expanded in z around 0 87.2%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right) + b}}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0026 \lor \neg \left(z \leq 4.2 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 11: 80.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-5} \lor \neg \left(z \leq 3.8 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - x \cdot \left(y \cdot -9\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2e-5) (not (<= z 3.8e+62)))
   (/ (+ (/ b z) (* -4.0 (* t a))) c)
   (/ (- b (* x (* y -9.0))) (* z c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2e-5) || !(z <= 3.8e+62)) {
		tmp = ((b / z) + (-4.0 * (t * a))) / c;
	} else {
		tmp = (b - (x * (y * -9.0))) / (z * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-2d-5)) .or. (.not. (z <= 3.8d+62))) then
        tmp = ((b / z) + ((-4.0d0) * (t * a))) / c
    else
        tmp = (b - (x * (y * (-9.0d0)))) / (z * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2e-5) || !(z <= 3.8e+62)) {
		tmp = ((b / z) + (-4.0 * (t * a))) / c;
	} else {
		tmp = (b - (x * (y * -9.0))) / (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -2e-5) or not (z <= 3.8e+62):
		tmp = ((b / z) + (-4.0 * (t * a))) / c
	else:
		tmp = (b - (x * (y * -9.0))) / (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -2e-5) || !(z <= 3.8e+62))
		tmp = Float64(Float64(Float64(b / z) + Float64(-4.0 * Float64(t * a))) / c);
	else
		tmp = Float64(Float64(b - Float64(x * Float64(y * -9.0))) / Float64(z * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -2e-5) || ~((z <= 3.8e+62)))
		tmp = ((b / z) + (-4.0 * (t * a))) / c;
	else
		tmp = (b - (x * (y * -9.0))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2e-5], N[Not[LessEqual[z, 3.8e+62]], $MachinePrecision]], N[(N[(N[(b / z), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b - N[(x * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000016e-5 or 3.79999999999999984e62 < z

   1. Initial program 88.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 87.2%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 94.1%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in x around 0 81.1%

      \[\leadsto \frac{\color{blue}{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}}{c} \]

   if -2.00000000000000016e-5 < z < 3.79999999999999984e62

   1. Initial program 96.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 89.5%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.3%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in t around 0 76.8%

      \[\leadsto \frac{\color{blue}{\frac{b}{z} + 9 \cdot \frac{y \cdot x}{z}}}{c} \]

   5. Taylor expanded in z around -inf 87.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{-9 \cdot \left(y \cdot x\right) + -1 \cdot b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 87.2%

         \[\leadsto \color{blue}{-\frac{-9 \cdot \left(y \cdot x\right) + -1 \cdot b}{c \cdot z}} \]

      2. distribute-neg-frac 87.2%

         \[\leadsto \color{blue}{\frac{-\left(-9 \cdot \left(y \cdot x\right) + -1 \cdot b\right)}{c \cdot z}} \]

      3. neg-mul-1 87.2%

         \[\leadsto \frac{-\left(-9 \cdot \left(y \cdot x\right) + \color{blue}{\left(-b\right)}\right)}{c \cdot z} \]

      4. unsub-neg 87.2%

         \[\leadsto \frac{-\color{blue}{\left(-9 \cdot \left(y \cdot x\right) - b\right)}}{c \cdot z} \]

      5. *-commutative 87.2%

         \[\leadsto \frac{-\left(\color{blue}{\left(y \cdot x\right) \cdot -9} - b\right)}{c \cdot z} \]

      6. associate-*l* 87.2%

         \[\leadsto \frac{-\left(\color{blue}{y \cdot \left(x \cdot -9\right)} - b\right)}{c \cdot z} \]

      7. *-commutative 87.2%

         \[\leadsto \frac{-\left(y \cdot \left(x \cdot -9\right) - b\right)}{\color{blue}{z \cdot c}} \]

   7. Simplified 87.2%

      \[\leadsto \color{blue}{\frac{-\left(y \cdot \left(x \cdot -9\right) - b\right)}{z \cdot c}} \]

   8. Taylor expanded in z around 0 87.2%

      \[\leadsto \color{blue}{\frac{b - -9 \cdot \left(y \cdot x\right)}{c \cdot z}} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 65.1%

         \[\leadsto \frac{b - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-9 \cdot \left(y \cdot x\right)\right)\right)}}{c \cdot z} \]

      2. expm1-udef 59.9%

         \[\leadsto \frac{b - \color{blue}{\left(e^{\mathsf{log1p}\left(-9 \cdot \left(y \cdot x\right)\right)} - 1\right)}}{c \cdot z} \]

   10. Applied egg-rr 59.9%

       \[\leadsto \frac{b - \color{blue}{\left(e^{\mathsf{log1p}\left(-9 \cdot \left(y \cdot x\right)\right)} - 1\right)}}{c \cdot z} \]
   11. Step-by-step derivation

       1. expm1-def 65.1%

          \[\leadsto \frac{b - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-9 \cdot \left(y \cdot x\right)\right)\right)}}{c \cdot z} \]

       2. expm1-log1p 87.2%

          \[\leadsto \frac{b - \color{blue}{-9 \cdot \left(y \cdot x\right)}}{c \cdot z} \]

       3. *-commutative 87.2%

          \[\leadsto \frac{b - \color{blue}{\left(y \cdot x\right) \cdot -9}}{c \cdot z} \]

       4. *-commutative 87.2%

          \[\leadsto \frac{b - \color{blue}{\left(x \cdot y\right)} \cdot -9}{c \cdot z} \]

       5. associate-*l* 87.2%

          \[\leadsto \frac{b - \color{blue}{x \cdot \left(y \cdot -9\right)}}{c \cdot z} \]

   12. Simplified 87.2%

       \[\leadsto \frac{b - \color{blue}{x \cdot \left(y \cdot -9\right)}}{c \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-5} \lor \neg \left(z \leq 3.8 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - x \cdot \left(y \cdot -9\right)}{z \cdot c}\\ \end{array} \]

Alternative 12: 52.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.85 \cdot 10^{-57} \lor \neg \left(b \leq 4.4 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -1.85e-57) (not (<= b 4.4e-27)))
   (/ b (* z c))
   (* -4.0 (* t (/ a c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.85e-57) || !(b <= 4.4e-27)) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-1.85d-57)) .or. (.not. (b <= 4.4d-27))) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.85e-57) || !(b <= 4.4e-27)) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -1.85e-57) or not (b <= 4.4e-27):
		tmp = b / (z * c)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -1.85e-57) || !(b <= 4.4e-27))
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -1.85e-57) || ~((b <= 4.4e-27)))
		tmp = b / (z * c);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -1.85e-57], N[Not[LessEqual[b, 4.4e-27]], $MachinePrecision]], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.85e-57 or 4.39999999999999974e-27 < b

   1. Initial program 96.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

   3. Simplified 97.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c}} \]

   4. Taylor expanded in b around inf 64.4%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 64.4%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 64.4%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if -1.85e-57 < b < 4.39999999999999974e-27

   1. Initial program 92.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

   3. Simplified 94.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c}} \]

   4. Taylor expanded in z around inf 42.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. associate-/l* 42.5%

         \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

      2. associate-/r/ 44.2%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

   6. Simplified 44.2%

      \[\leadsto \color{blue}{-4 \cdot \left(\frac{a}{c} \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.85 \cdot 10^{-57} \lor \neg \left(b \leq 4.4 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 13: 52.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-52} \lor \neg \left(b \leq 2.5 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -1.5e-52) (not (<= b 2.5e-26)))
   (/ b (* z c))
   (* -4.0 (/ a (/ c t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.5e-52) || !(b <= 2.5e-26)) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-1.5d-52)) .or. (.not. (b <= 2.5d-26))) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * (a / (c / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.5e-52) || !(b <= 2.5e-26)) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -1.5e-52) or not (b <= 2.5e-26):
		tmp = b / (z * c)
	else:
		tmp = -4.0 * (a / (c / t))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -1.5e-52) || !(b <= 2.5e-26))
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -1.5e-52) || ~((b <= 2.5e-26)))
		tmp = b / (z * c);
	else
		tmp = -4.0 * (a / (c / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -1.5e-52], N[Not[LessEqual[b, 2.5e-26]], $MachinePrecision]], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.5e-52 or 2.5000000000000001e-26 < b

   1. Initial program 96.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

   3. Simplified 97.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c}} \]

   4. Taylor expanded in b around inf 64.8%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 64.8%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 64.8%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if -1.5e-52 < b < 2.5000000000000001e-26

   1. Initial program 92.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

   3. Simplified 94.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c}} \]

   4. Taylor expanded in z around inf 43.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. associate-/l* 43.0%

         \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

   6. Simplified 43.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a}{\frac{c}{t}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-52} \lor \neg \left(b \leq 2.5 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 14: 44.2% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return b / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.7%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

3. Simplified 96.1%

   \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(z, t \cdot \left(-4 \cdot a\right), b\right)\right)}{z \cdot c}} \]

4. Taylor expanded in b around inf 42.5%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
5. Step-by-step derivation

   1. *-commutative 42.5%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

6. Simplified 42.5%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

7. Final simplification 42.5%

   \[\leadsto \frac{b}{z \cdot c} \]

Developer target: 85.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t_4}{z \cdot c}\\ t_6 := \frac{\left(t_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 < 0:\\ \;\;\;\;\frac{\frac{t_4}{z}}{c}\\ \mathbf{elif}\;t_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t_1\right) - t_2\\ \mathbf{elif}\;t_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t_1\right) - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2023278 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :herbie-target
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))