Data.Colour.RGB:hslsv from colour-2.3.3, B

Percentage Accurate: 99.4% → 99.4%

Time: 13.9s

Alternatives: 20

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 59.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.4 \cdot 10^{-94}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-256}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-141}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-83}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.4e-94)
   (* a 120.0)
   (if (<= a -4.8e-256)
     (/ (* 60.0 x) (- z t))
     (if (<= a 6.5e-141)
       (* (- x y) (/ -60.0 t))
       (if (<= a 1.6e-83) (/ (* y -60.0) (- z t)) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.4e-94) {
		tmp = a * 120.0;
	} else if (a <= -4.8e-256) {
		tmp = (60.0 * x) / (z - t);
	} else if (a <= 6.5e-141) {
		tmp = (x - y) * (-60.0 / t);
	} else if (a <= 1.6e-83) {
		tmp = (y * -60.0) / (z - t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (a <= (-7.4d-94)) then
        tmp = a * 120.0d0
    else if (a <= (-4.8d-256)) then
        tmp = (60.0d0 * x) / (z - t)
    else if (a <= 6.5d-141) then
        tmp = (x - y) * ((-60.0d0) / t)
    else if (a <= 1.6d-83) then
        tmp = (y * (-60.0d0)) / (z - t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.4e-94) {
		tmp = a * 120.0;
	} else if (a <= -4.8e-256) {
		tmp = (60.0 * x) / (z - t);
	} else if (a <= 6.5e-141) {
		tmp = (x - y) * (-60.0 / t);
	} else if (a <= 1.6e-83) {
		tmp = (y * -60.0) / (z - t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.4e-94:
		tmp = a * 120.0
	elif a <= -4.8e-256:
		tmp = (60.0 * x) / (z - t)
	elif a <= 6.5e-141:
		tmp = (x - y) * (-60.0 / t)
	elif a <= 1.6e-83:
		tmp = (y * -60.0) / (z - t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.4e-94)
		tmp = Float64(a * 120.0);
	elseif (a <= -4.8e-256)
		tmp = Float64(Float64(60.0 * x) / Float64(z - t));
	elseif (a <= 6.5e-141)
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	elseif (a <= 1.6e-83)
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.4e-94)
		tmp = a * 120.0;
	elseif (a <= -4.8e-256)
		tmp = (60.0 * x) / (z - t);
	elseif (a <= 6.5e-141)
		tmp = (x - y) * (-60.0 / t);
	elseif (a <= 1.6e-83)
		tmp = (y * -60.0) / (z - t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.4e-94], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -4.8e-256], N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-141], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e-83], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.3999999999999996e-94 or 1.6000000000000001e-83 < a

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} + a \cdot 120 \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{60}{z - t}, a \cdot 120\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{z + \left(-t\right)}}, a \cdot 120\right) \]

      5. +-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(-t\right) + z}}, a \cdot 120\right) \]

      6. neg-sub0 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(0 - t\right)} + z}, a \cdot 120\right) \]

      7. associate-+l- 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{0 - \left(t - z\right)}}, a \cdot 120\right) \]

      8. sub0-neg 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{-\left(t - z\right)}}, a \cdot 120\right) \]

      9. distribute-frac-neg2 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{-\frac{60}{t - z}}, a \cdot 120\right) \]

      10. distribute-neg-frac 99.8%

          \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{\frac{-60}{t - z}}, a \cdot 120\right) \]

      11. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x - y, \frac{\color{blue}{-60}}{t - z}, a \cdot 120\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{-60}{t - z}, a \cdot 120\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 65.9%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -7.3999999999999996e-94 < a < -4.7999999999999999e-256

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{a \cdot 120 + 60 \cdot \frac{x - y}{z - t}} \]

      2. fma-define 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, 60 \cdot \frac{x - y}{z - t}\right)} \]

      3. clear-num 99.5%

         \[\leadsto \mathsf{fma}\left(a, 120, 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}}\right) \]

      4. un-div-inv 99.7%

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{\frac{z - t}{x - y}}}\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)} \]

   7. Taylor expanded in x around inf 55.9%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 56.0%

         \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} \]

   9. Simplified 56.0%

      \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} \]

   if -4.7999999999999999e-256 < a < 6.4999999999999995e-141

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.5%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 99.5%

         \[\leadsto \color{blue}{a \cdot 120 + 60 \cdot \frac{x - y}{z - t}} \]

      2. fma-define 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, 60 \cdot \frac{x - y}{z - t}\right)} \]

      3. clear-num 99.6%

         \[\leadsto \mathsf{fma}\left(a, 120, 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}}\right) \]

      4. un-div-inv 99.7%

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{\frac{z - t}{x - y}}}\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)} \]

   7. Taylor expanded in a around 0 91.3%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 91.3%

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      2. associate-*l/ 91.3%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} \]

      3. metadata-eval 91.3%

         \[\leadsto \frac{\color{blue}{60 \cdot 1}}{z - t} \cdot \left(x - y\right) \]

      4. associate-*r/ 91.1%

         \[\leadsto \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)} \cdot \left(x - y\right) \]

      5. *-commutative 91.1%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      6. associate-*r/ 91.3%

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{60 \cdot 1}{z - t}} \]

      7. metadata-eval 91.3%

         \[\leadsto \left(x - y\right) \cdot \frac{\color{blue}{60}}{z - t} \]

   9. Simplified 91.3%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} \]

   10. Taylor expanded in z around 0 58.5%

       \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{-60}{t}} \]

   if 6.4999999999999995e-141 < a < 1.6000000000000001e-83

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.5%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 99.5%

         \[\leadsto \color{blue}{a \cdot 120 + 60 \cdot \frac{x - y}{z - t}} \]

      2. fma-define 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, 60 \cdot \frac{x - y}{z - t}\right)} \]

      3. clear-num 99.7%

         \[\leadsto \mathsf{fma}\left(a, 120, 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}}\right) \]

      4. un-div-inv 99.9%

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{\frac{z - t}{x - y}}}\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)} \]

   7. Taylor expanded in y around inf 75.4%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 75.6%

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} \]

      2. *-commutative 75.6%

         \[\leadsto \frac{\color{blue}{y \cdot -60}}{z - t} \]

   9. Simplified 75.6%

      \[\leadsto \color{blue}{\frac{y \cdot -60}{z - t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.4 \cdot 10^{-94}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-256}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-141}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-83}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-93}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-256}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-140}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-82}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e-93)
   (* a 120.0)
   (if (<= a -1e-256)
     (/ (* 60.0 x) (- z t))
     (if (<= a 1.7e-140)
       (* (- x y) (/ -60.0 t))
       (if (<= a 1.7e-82) (* 60.0 (/ y (- t z))) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e-93) {
		tmp = a * 120.0;
	} else if (a <= -1e-256) {
		tmp = (60.0 * x) / (z - t);
	} else if (a <= 1.7e-140) {
		tmp = (x - y) * (-60.0 / t);
	} else if (a <= 1.7e-82) {
		tmp = 60.0 * (y / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (a <= (-1.2d-93)) then
        tmp = a * 120.0d0
    else if (a <= (-1d-256)) then
        tmp = (60.0d0 * x) / (z - t)
    else if (a <= 1.7d-140) then
        tmp = (x - y) * ((-60.0d0) / t)
    else if (a <= 1.7d-82) then
        tmp = 60.0d0 * (y / (t - z))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e-93) {
		tmp = a * 120.0;
	} else if (a <= -1e-256) {
		tmp = (60.0 * x) / (z - t);
	} else if (a <= 1.7e-140) {
		tmp = (x - y) * (-60.0 / t);
	} else if (a <= 1.7e-82) {
		tmp = 60.0 * (y / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.2e-93:
		tmp = a * 120.0
	elif a <= -1e-256:
		tmp = (60.0 * x) / (z - t)
	elif a <= 1.7e-140:
		tmp = (x - y) * (-60.0 / t)
	elif a <= 1.7e-82:
		tmp = 60.0 * (y / (t - z))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e-93)
		tmp = Float64(a * 120.0);
	elseif (a <= -1e-256)
		tmp = Float64(Float64(60.0 * x) / Float64(z - t));
	elseif (a <= 1.7e-140)
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	elseif (a <= 1.7e-82)
		tmp = Float64(60.0 * Float64(y / Float64(t - z)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.2e-93)
		tmp = a * 120.0;
	elseif (a <= -1e-256)
		tmp = (60.0 * x) / (z - t);
	elseif (a <= 1.7e-140)
		tmp = (x - y) * (-60.0 / t);
	elseif (a <= 1.7e-82)
		tmp = 60.0 * (y / (t - z));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e-93], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1e-256], N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e-140], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e-82], N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.2000000000000001e-93 or 1.69999999999999988e-82 < a

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} + a \cdot 120 \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{60}{z - t}, a \cdot 120\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{z + \left(-t\right)}}, a \cdot 120\right) \]

      5. +-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(-t\right) + z}}, a \cdot 120\right) \]

      6. neg-sub0 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(0 - t\right)} + z}, a \cdot 120\right) \]

      7. associate-+l- 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{0 - \left(t - z\right)}}, a \cdot 120\right) \]

      8. sub0-neg 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{-\left(t - z\right)}}, a \cdot 120\right) \]

      9. distribute-frac-neg2 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{-\frac{60}{t - z}}, a \cdot 120\right) \]

      10. distribute-neg-frac 99.8%

          \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{\frac{-60}{t - z}}, a \cdot 120\right) \]

      11. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x - y, \frac{\color{blue}{-60}}{t - z}, a \cdot 120\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{-60}{t - z}, a \cdot 120\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 65.9%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -1.2000000000000001e-93 < a < -9.99999999999999977e-257

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{a \cdot 120 + 60 \cdot \frac{x - y}{z - t}} \]

      2. fma-define 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, 60 \cdot \frac{x - y}{z - t}\right)} \]

      3. clear-num 99.5%

         \[\leadsto \mathsf{fma}\left(a, 120, 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}}\right) \]

      4. un-div-inv 99.7%

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{\frac{z - t}{x - y}}}\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)} \]

   7. Taylor expanded in x around inf 55.9%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 56.0%

         \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} \]

   9. Simplified 56.0%

      \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} \]

   if -9.99999999999999977e-257 < a < 1.70000000000000004e-140

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.5%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 99.5%

         \[\leadsto \color{blue}{a \cdot 120 + 60 \cdot \frac{x - y}{z - t}} \]

      2. fma-define 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, 60 \cdot \frac{x - y}{z - t}\right)} \]

      3. clear-num 99.6%

         \[\leadsto \mathsf{fma}\left(a, 120, 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}}\right) \]

      4. un-div-inv 99.7%

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{\frac{z - t}{x - y}}}\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)} \]

   7. Taylor expanded in a around 0 91.3%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 91.3%

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      2. associate-*l/ 91.3%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} \]

      3. metadata-eval 91.3%

         \[\leadsto \frac{\color{blue}{60 \cdot 1}}{z - t} \cdot \left(x - y\right) \]

      4. associate-*r/ 91.1%

         \[\leadsto \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)} \cdot \left(x - y\right) \]

      5. *-commutative 91.1%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      6. associate-*r/ 91.3%

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{60 \cdot 1}{z - t}} \]

      7. metadata-eval 91.3%

         \[\leadsto \left(x - y\right) \cdot \frac{\color{blue}{60}}{z - t} \]

   9. Simplified 91.3%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} \]

   10. Taylor expanded in z around 0 58.5%

       \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{-60}{t}} \]

   if 1.70000000000000004e-140 < a < 1.69999999999999988e-82

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. *-commutative 99.7%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.6%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} + a \cdot 120 \]

      3. fma-define 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{60}{z - t}, a \cdot 120\right)} \]

      4. sub-neg 99.6%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{z + \left(-t\right)}}, a \cdot 120\right) \]

      5. +-commutative 99.6%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(-t\right) + z}}, a \cdot 120\right) \]

      6. neg-sub0 99.6%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(0 - t\right)} + z}, a \cdot 120\right) \]

      7. associate-+l- 99.6%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{0 - \left(t - z\right)}}, a \cdot 120\right) \]

      8. sub0-neg 99.6%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{-\left(t - z\right)}}, a \cdot 120\right) \]

      9. distribute-frac-neg2 99.6%

         \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{-\frac{60}{t - z}}, a \cdot 120\right) \]

      10. distribute-neg-frac 99.6%

          \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{\frac{-60}{t - z}}, a \cdot 120\right) \]

      11. metadata-eval 99.6%

          \[\leadsto \mathsf{fma}\left(x - y, \frac{\color{blue}{-60}}{t - z}, a \cdot 120\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{-60}{t - z}, a \cdot 120\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 75.4%

      \[\leadsto \color{blue}{60 \cdot \frac{y}{t - z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-93}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-256}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-140}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-82}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-101}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-255}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-141}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-82}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.5e-101)
   (* a 120.0)
   (if (<= a -1.15e-255)
     (* 60.0 (/ x (- z t)))
     (if (<= a 1.8e-141)
       (* (- x y) (/ -60.0 t))
       (if (<= a 1.12e-82) (* 60.0 (/ y (- t z))) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.5e-101) {
		tmp = a * 120.0;
	} else if (a <= -1.15e-255) {
		tmp = 60.0 * (x / (z - t));
	} else if (a <= 1.8e-141) {
		tmp = (x - y) * (-60.0 / t);
	} else if (a <= 1.12e-82) {
		tmp = 60.0 * (y / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (a <= (-1.5d-101)) then
        tmp = a * 120.0d0
    else if (a <= (-1.15d-255)) then
        tmp = 60.0d0 * (x / (z - t))
    else if (a <= 1.8d-141) then
        tmp = (x - y) * ((-60.0d0) / t)
    else if (a <= 1.12d-82) then
        tmp = 60.0d0 * (y / (t - z))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.5e-101) {
		tmp = a * 120.0;
	} else if (a <= -1.15e-255) {
		tmp = 60.0 * (x / (z - t));
	} else if (a <= 1.8e-141) {
		tmp = (x - y) * (-60.0 / t);
	} else if (a <= 1.12e-82) {
		tmp = 60.0 * (y / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.5e-101:
		tmp = a * 120.0
	elif a <= -1.15e-255:
		tmp = 60.0 * (x / (z - t))
	elif a <= 1.8e-141:
		tmp = (x - y) * (-60.0 / t)
	elif a <= 1.12e-82:
		tmp = 60.0 * (y / (t - z))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.5e-101)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.15e-255)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	elseif (a <= 1.8e-141)
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	elseif (a <= 1.12e-82)
		tmp = Float64(60.0 * Float64(y / Float64(t - z)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.5e-101)
		tmp = a * 120.0;
	elseif (a <= -1.15e-255)
		tmp = 60.0 * (x / (z - t));
	elseif (a <= 1.8e-141)
		tmp = (x - y) * (-60.0 / t);
	elseif (a <= 1.12e-82)
		tmp = 60.0 * (y / (t - z));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.5e-101], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.15e-255], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e-141], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.12e-82], N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.5000000000000002e-101 or 1.12e-82 < a

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} + a \cdot 120 \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{60}{z - t}, a \cdot 120\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{z + \left(-t\right)}}, a \cdot 120\right) \]

      5. +-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(-t\right) + z}}, a \cdot 120\right) \]

      6. neg-sub0 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(0 - t\right)} + z}, a \cdot 120\right) \]

      7. associate-+l- 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{0 - \left(t - z\right)}}, a \cdot 120\right) \]

      8. sub0-neg 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{-\left(t - z\right)}}, a \cdot 120\right) \]

      9. distribute-frac-neg2 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{-\frac{60}{t - z}}, a \cdot 120\right) \]

      10. distribute-neg-frac 99.8%

          \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{\frac{-60}{t - z}}, a \cdot 120\right) \]

      11. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x - y, \frac{\color{blue}{-60}}{t - z}, a \cdot 120\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{-60}{t - z}, a \cdot 120\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 65.9%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -1.5000000000000002e-101 < a < -1.1499999999999999e-255

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{a \cdot 120 + 60 \cdot \frac{x - y}{z - t}} \]

      2. fma-define 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, 60 \cdot \frac{x - y}{z - t}\right)} \]

      3. clear-num 99.5%

         \[\leadsto \mathsf{fma}\left(a, 120, 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}}\right) \]

      4. un-div-inv 99.7%

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{\frac{z - t}{x - y}}}\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)} \]

   7. Taylor expanded in x around inf 55.9%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]

   if -1.1499999999999999e-255 < a < 1.80000000000000007e-141

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.5%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 99.5%

         \[\leadsto \color{blue}{a \cdot 120 + 60 \cdot \frac{x - y}{z - t}} \]

      2. fma-define 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, 60 \cdot \frac{x - y}{z - t}\right)} \]

      3. clear-num 99.6%

         \[\leadsto \mathsf{fma}\left(a, 120, 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}}\right) \]

      4. un-div-inv 99.7%

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{\frac{z - t}{x - y}}}\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)} \]

   7. Taylor expanded in a around 0 91.3%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 91.3%

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      2. associate-*l/ 91.3%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} \]

      3. metadata-eval 91.3%

         \[\leadsto \frac{\color{blue}{60 \cdot 1}}{z - t} \cdot \left(x - y\right) \]

      4. associate-*r/ 91.1%

         \[\leadsto \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)} \cdot \left(x - y\right) \]

      5. *-commutative 91.1%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      6. associate-*r/ 91.3%

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{60 \cdot 1}{z - t}} \]

      7. metadata-eval 91.3%

         \[\leadsto \left(x - y\right) \cdot \frac{\color{blue}{60}}{z - t} \]

   9. Simplified 91.3%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} \]

   10. Taylor expanded in z around 0 58.5%

       \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{-60}{t}} \]

   if 1.80000000000000007e-141 < a < 1.12e-82

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. *-commutative 99.7%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.6%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} + a \cdot 120 \]

      3. fma-define 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{60}{z - t}, a \cdot 120\right)} \]

      4. sub-neg 99.6%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{z + \left(-t\right)}}, a \cdot 120\right) \]

      5. +-commutative 99.6%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(-t\right) + z}}, a \cdot 120\right) \]

      6. neg-sub0 99.6%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(0 - t\right)} + z}, a \cdot 120\right) \]

      7. associate-+l- 99.6%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{0 - \left(t - z\right)}}, a \cdot 120\right) \]

      8. sub0-neg 99.6%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{-\left(t - z\right)}}, a \cdot 120\right) \]

      9. distribute-frac-neg2 99.6%

         \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{-\frac{60}{t - z}}, a \cdot 120\right) \]

      10. distribute-neg-frac 99.6%

          \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{\frac{-60}{t - z}}, a \cdot 120\right) \]

      11. metadata-eval 99.6%

          \[\leadsto \mathsf{fma}\left(x - y, \frac{\color{blue}{-60}}{t - z}, a \cdot 120\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{-60}{t - z}, a \cdot 120\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 75.4%

      \[\leadsto \color{blue}{60 \cdot \frac{y}{t - z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-101}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-255}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-141}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-82}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-83} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{-140}\right):\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -2e-83) (not (<= (* a 120.0) 2e-140)))
   (+ (* a 120.0) (* y (/ -60.0 (- z t))))
   (* (- x y) (/ 60.0 (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2e-83) || !((a * 120.0) <= 2e-140)) {
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (((a * 120.0d0) <= (-2d-83)) .or. (.not. ((a * 120.0d0) <= 2d-140))) then
        tmp = (a * 120.0d0) + (y * ((-60.0d0) / (z - t)))
    else
        tmp = (x - y) * (60.0d0 / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2e-83) || !((a * 120.0) <= 2e-140)) {
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -2e-83) or not ((a * 120.0) <= 2e-140):
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)))
	else:
		tmp = (x - y) * (60.0 / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -2e-83) || !(Float64(a * 120.0) <= 2e-140))
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(-60.0 / Float64(z - t))));
	else
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -2e-83) || ~(((a * 120.0) <= 2e-140)))
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	else
		tmp = (x - y) * (60.0 / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-83], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-140]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -2.0000000000000001e-83 or 2e-140 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 87.9%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} + a \cdot 120 \]
   6. Step-by-step derivation

      1. associate-*r/ 87.9%

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} + a \cdot 120 \]

      2. *-commutative 87.9%

         \[\leadsto \frac{\color{blue}{y \cdot -60}}{z - t} + a \cdot 120 \]

      3. *-lft-identity 87.9%

         \[\leadsto \frac{y \cdot -60}{\color{blue}{1 \cdot \left(z - t\right)}} + a \cdot 120 \]

      4. times-frac 87.9%

         \[\leadsto \color{blue}{\frac{y}{1} \cdot \frac{-60}{z - t}} + a \cdot 120 \]

      5. /-rgt-identity 87.9%

         \[\leadsto \color{blue}{y} \cdot \frac{-60}{z - t} + a \cdot 120 \]

   7. Simplified 87.9%

      \[\leadsto \color{blue}{y \cdot \frac{-60}{z - t}} + a \cdot 120 \]

   if -2.0000000000000001e-83 < (*.f64 a #s(literal 120 binary64)) < 2e-140

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{a \cdot 120 + 60 \cdot \frac{x - y}{z - t}} \]

      2. fma-define 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, 60 \cdot \frac{x - y}{z - t}\right)} \]

      3. clear-num 99.5%

         \[\leadsto \mathsf{fma}\left(a, 120, 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}}\right) \]

      4. un-div-inv 99.7%

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{\frac{z - t}{x - y}}}\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)} \]

   7. Taylor expanded in a around 0 86.7%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 86.8%

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      2. associate-*l/ 86.8%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} \]

      3. metadata-eval 86.8%

         \[\leadsto \frac{\color{blue}{60 \cdot 1}}{z - t} \cdot \left(x - y\right) \]

      4. associate-*r/ 86.6%

         \[\leadsto \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)} \cdot \left(x - y\right) \]

      5. *-commutative 86.6%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      6. associate-*r/ 86.8%

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{60 \cdot 1}{z - t}} \]

      7. metadata-eval 86.8%

         \[\leadsto \left(x - y\right) \cdot \frac{\color{blue}{60}}{z - t} \]

   9. Simplified 86.8%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-83} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{-140}\right):\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -100000000 \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{-28}\right):\\ \;\;\;\;a \cdot 120 + y \cdot \frac{60}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -100000000.0) (not (<= (* a 120.0) 2e-28)))
   (+ (* a 120.0) (* y (/ 60.0 t)))
   (* (- x y) (/ 60.0 (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -100000000.0) || !((a * 120.0) <= 2e-28)) {
		tmp = (a * 120.0) + (y * (60.0 / t));
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (((a * 120.0d0) <= (-100000000.0d0)) .or. (.not. ((a * 120.0d0) <= 2d-28))) then
        tmp = (a * 120.0d0) + (y * (60.0d0 / t))
    else
        tmp = (x - y) * (60.0d0 / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -100000000.0) || !((a * 120.0) <= 2e-28)) {
		tmp = (a * 120.0) + (y * (60.0 / t));
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -100000000.0) or not ((a * 120.0) <= 2e-28):
		tmp = (a * 120.0) + (y * (60.0 / t))
	else:
		tmp = (x - y) * (60.0 / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -100000000.0) || !(Float64(a * 120.0) <= 2e-28))
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(60.0 / t)));
	else
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -100000000.0) || ~(((a * 120.0) <= 2e-28)))
		tmp = (a * 120.0) + (y * (60.0 / t));
	else
		tmp = (x - y) * (60.0 / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -100000000.0], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-28]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1e8 or 1.99999999999999994e-28 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 90.8%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} + a \cdot 120 \]
   6. Step-by-step derivation

      1. associate-*r/ 90.8%

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} + a \cdot 120 \]

      2. *-commutative 90.8%

         \[\leadsto \frac{\color{blue}{y \cdot -60}}{z - t} + a \cdot 120 \]

      3. *-lft-identity 90.8%

         \[\leadsto \frac{y \cdot -60}{\color{blue}{1 \cdot \left(z - t\right)}} + a \cdot 120 \]

      4. times-frac 90.8%

         \[\leadsto \color{blue}{\frac{y}{1} \cdot \frac{-60}{z - t}} + a \cdot 120 \]

      5. /-rgt-identity 90.8%

         \[\leadsto \color{blue}{y} \cdot \frac{-60}{z - t} + a \cdot 120 \]

   7. Simplified 90.8%

      \[\leadsto \color{blue}{y \cdot \frac{-60}{z - t}} + a \cdot 120 \]

   8. Taylor expanded in z around 0 75.7%

      \[\leadsto y \cdot \color{blue}{\frac{60}{t}} + a \cdot 120 \]

   if -1e8 < (*.f64 a #s(literal 120 binary64)) < 1.99999999999999994e-28

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{a \cdot 120 + 60 \cdot \frac{x - y}{z - t}} \]

      2. fma-define 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, 60 \cdot \frac{x - y}{z - t}\right)} \]

      3. clear-num 99.6%

         \[\leadsto \mathsf{fma}\left(a, 120, 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}}\right) \]

      4. un-div-inv 99.7%

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{\frac{z - t}{x - y}}}\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)} \]

   7. Taylor expanded in a around 0 79.3%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 79.4%

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      2. associate-*l/ 79.4%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} \]

      3. metadata-eval 79.4%

         \[\leadsto \frac{\color{blue}{60 \cdot 1}}{z - t} \cdot \left(x - y\right) \]

      4. associate-*r/ 79.2%

         \[\leadsto \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)} \cdot \left(x - y\right) \]

      5. *-commutative 79.2%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      6. associate-*r/ 79.4%

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{60 \cdot 1}{z - t}} \]

      7. metadata-eval 79.4%

         \[\leadsto \left(x - y\right) \cdot \frac{\color{blue}{60}}{z - t} \]

   9. Simplified 79.4%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -100000000 \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{-28}\right):\\ \;\;\;\;a \cdot 120 + y \cdot \frac{60}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -10000 \lor \neg \left(a \cdot 120 \leq 4 \cdot 10^{+32}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -10000.0) (not (<= (* a 120.0) 4e+32)))
   (* a 120.0)
   (* (- x y) (/ 60.0 (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -10000.0) || !((a * 120.0) <= 4e+32)) {
		tmp = a * 120.0;
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (((a * 120.0d0) <= (-10000.0d0)) .or. (.not. ((a * 120.0d0) <= 4d+32))) then
        tmp = a * 120.0d0
    else
        tmp = (x - y) * (60.0d0 / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -10000.0) || !((a * 120.0) <= 4e+32)) {
		tmp = a * 120.0;
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -10000.0) or not ((a * 120.0) <= 4e+32):
		tmp = a * 120.0
	else:
		tmp = (x - y) * (60.0 / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -10000.0) || !(Float64(a * 120.0) <= 4e+32))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -10000.0) || ~(((a * 120.0) <= 4e+32)))
		tmp = a * 120.0;
	else
		tmp = (x - y) * (60.0 / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -10000.0], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 4e+32]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1e4 or 4.00000000000000021e32 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} + a \cdot 120 \]

      3. fma-define 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{60}{z - t}, a \cdot 120\right)} \]

      4. sub-neg 99.9%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{z + \left(-t\right)}}, a \cdot 120\right) \]

      5. +-commutative 99.9%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(-t\right) + z}}, a \cdot 120\right) \]

      6. neg-sub0 99.9%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(0 - t\right)} + z}, a \cdot 120\right) \]

      7. associate-+l- 99.9%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{0 - \left(t - z\right)}}, a \cdot 120\right) \]

      8. sub0-neg 99.9%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{-\left(t - z\right)}}, a \cdot 120\right) \]

      9. distribute-frac-neg2 99.9%

         \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{-\frac{60}{t - z}}, a \cdot 120\right) \]

      10. distribute-neg-frac 99.9%

          \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{\frac{-60}{t - z}}, a \cdot 120\right) \]

      11. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(x - y, \frac{\color{blue}{-60}}{t - z}, a \cdot 120\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{-60}{t - z}, a \cdot 120\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 73.7%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -1e4 < (*.f64 a #s(literal 120 binary64)) < 4.00000000000000021e32

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{a \cdot 120 + 60 \cdot \frac{x - y}{z - t}} \]

      2. fma-define 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, 60 \cdot \frac{x - y}{z - t}\right)} \]

      3. clear-num 99.6%

         \[\leadsto \mathsf{fma}\left(a, 120, 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}}\right) \]

      4. un-div-inv 99.7%

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{\frac{z - t}{x - y}}}\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)} \]

   7. Taylor expanded in a around 0 77.7%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 77.8%

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      2. associate-*l/ 77.8%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} \]

      3. metadata-eval 77.8%

         \[\leadsto \frac{\color{blue}{60 \cdot 1}}{z - t} \cdot \left(x - y\right) \]

      4. associate-*r/ 77.6%

         \[\leadsto \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)} \cdot \left(x - y\right) \]

      5. *-commutative 77.6%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      6. associate-*r/ 77.8%

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{60 \cdot 1}{z - t}} \]

      7. metadata-eval 77.8%

         \[\leadsto \left(x - y\right) \cdot \frac{\color{blue}{60}}{z - t} \]

   9. Simplified 77.8%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -10000 \lor \neg \left(a \cdot 120 \leq 4 \cdot 10^{+32}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-99}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-259}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-83}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.45e-99)
   (* a 120.0)
   (if (<= a -4.8e-259)
     (* 60.0 (/ x (- z t)))
     (if (<= a 1.25e-83) (* 60.0 (/ y (- t z))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.45e-99) {
		tmp = a * 120.0;
	} else if (a <= -4.8e-259) {
		tmp = 60.0 * (x / (z - t));
	} else if (a <= 1.25e-83) {
		tmp = 60.0 * (y / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (a <= (-1.45d-99)) then
        tmp = a * 120.0d0
    else if (a <= (-4.8d-259)) then
        tmp = 60.0d0 * (x / (z - t))
    else if (a <= 1.25d-83) then
        tmp = 60.0d0 * (y / (t - z))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.45e-99) {
		tmp = a * 120.0;
	} else if (a <= -4.8e-259) {
		tmp = 60.0 * (x / (z - t));
	} else if (a <= 1.25e-83) {
		tmp = 60.0 * (y / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.45e-99:
		tmp = a * 120.0
	elif a <= -4.8e-259:
		tmp = 60.0 * (x / (z - t))
	elif a <= 1.25e-83:
		tmp = 60.0 * (y / (t - z))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.45e-99)
		tmp = Float64(a * 120.0);
	elseif (a <= -4.8e-259)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	elseif (a <= 1.25e-83)
		tmp = Float64(60.0 * Float64(y / Float64(t - z)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.45e-99)
		tmp = a * 120.0;
	elseif (a <= -4.8e-259)
		tmp = 60.0 * (x / (z - t));
	elseif (a <= 1.25e-83)
		tmp = 60.0 * (y / (t - z));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.45e-99], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -4.8e-259], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e-83], N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.44999999999999993e-99 or 1.25e-83 < a

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} + a \cdot 120 \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{60}{z - t}, a \cdot 120\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{z + \left(-t\right)}}, a \cdot 120\right) \]

      5. +-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(-t\right) + z}}, a \cdot 120\right) \]

      6. neg-sub0 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(0 - t\right)} + z}, a \cdot 120\right) \]

      7. associate-+l- 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{0 - \left(t - z\right)}}, a \cdot 120\right) \]

      8. sub0-neg 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{-\left(t - z\right)}}, a \cdot 120\right) \]

      9. distribute-frac-neg2 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{-\frac{60}{t - z}}, a \cdot 120\right) \]

      10. distribute-neg-frac 99.8%

          \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{\frac{-60}{t - z}}, a \cdot 120\right) \]

      11. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x - y, \frac{\color{blue}{-60}}{t - z}, a \cdot 120\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{-60}{t - z}, a \cdot 120\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 65.9%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -1.44999999999999993e-99 < a < -4.8000000000000001e-259

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{a \cdot 120 + 60 \cdot \frac{x - y}{z - t}} \]

      2. fma-define 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, 60 \cdot \frac{x - y}{z - t}\right)} \]

      3. clear-num 99.5%

         \[\leadsto \mathsf{fma}\left(a, 120, 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}}\right) \]

      4. un-div-inv 99.7%

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{\frac{z - t}{x - y}}}\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)} \]

   7. Taylor expanded in x around inf 55.9%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]

   if -4.8000000000000001e-259 < a < 1.25e-83

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. *-commutative 99.6%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.6%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} + a \cdot 120 \]

      3. fma-define 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{60}{z - t}, a \cdot 120\right)} \]

      4. sub-neg 99.6%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{z + \left(-t\right)}}, a \cdot 120\right) \]

      5. +-commutative 99.6%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(-t\right) + z}}, a \cdot 120\right) \]

      6. neg-sub0 99.6%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(0 - t\right)} + z}, a \cdot 120\right) \]

      7. associate-+l- 99.6%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{0 - \left(t - z\right)}}, a \cdot 120\right) \]

      8. sub0-neg 99.6%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{-\left(t - z\right)}}, a \cdot 120\right) \]

      9. distribute-frac-neg2 99.6%

         \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{-\frac{60}{t - z}}, a \cdot 120\right) \]

      10. distribute-neg-frac 99.6%

          \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{\frac{-60}{t - z}}, a \cdot 120\right) \]

      11. metadata-eval 99.6%

          \[\leadsto \mathsf{fma}\left(x - y, \frac{\color{blue}{-60}}{t - z}, a \cdot 120\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{-60}{t - z}, a \cdot 120\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 54.4%

      \[\leadsto \color{blue}{60 \cdot \frac{y}{t - z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-99}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-259}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-83}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+94} \lor \neg \left(y \leq 3.2 \cdot 10^{-10}\right):\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -6.6e+94) (not (<= y 3.2e-10)))
   (+ (* a 120.0) (* y (/ -60.0 (- z t))))
   (+ (* a 120.0) (/ 60.0 (/ (- z t) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.6e+94) || !(y <= 3.2e-10)) {
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	} else {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((y <= (-6.6d+94)) .or. (.not. (y <= 3.2d-10))) then
        tmp = (a * 120.0d0) + (y * ((-60.0d0) / (z - t)))
    else
        tmp = (a * 120.0d0) + (60.0d0 / ((z - t) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.6e+94) || !(y <= 3.2e-10)) {
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	} else {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -6.6e+94) or not (y <= 3.2e-10):
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)))
	else:
		tmp = (a * 120.0) + (60.0 / ((z - t) / x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -6.6e+94) || !(y <= 3.2e-10))
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(-60.0 / Float64(z - t))));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(z - t) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -6.6e+94) || ~((y <= 3.2e-10)))
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	else
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -6.6e+94], N[Not[LessEqual[y, 3.2e-10]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.6e94 or 3.19999999999999981e-10 < y

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 88.8%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} + a \cdot 120 \]
   6. Step-by-step derivation

      1. associate-*r/ 88.9%

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} + a \cdot 120 \]

      2. *-commutative 88.9%

         \[\leadsto \frac{\color{blue}{y \cdot -60}}{z - t} + a \cdot 120 \]

      3. *-lft-identity 88.9%

         \[\leadsto \frac{y \cdot -60}{\color{blue}{1 \cdot \left(z - t\right)}} + a \cdot 120 \]

      4. times-frac 88.8%

         \[\leadsto \color{blue}{\frac{y}{1} \cdot \frac{-60}{z - t}} + a \cdot 120 \]

      5. /-rgt-identity 88.8%

         \[\leadsto \color{blue}{y} \cdot \frac{-60}{z - t} + a \cdot 120 \]

   7. Simplified 88.8%

      \[\leadsto \color{blue}{y \cdot \frac{-60}{z - t}} + a \cdot 120 \]

   if -6.6e94 < y < 3.19999999999999981e-10

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.7%

         \[\leadsto 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}} + a \cdot 120 \]

      2. un-div-inv 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   7. Taylor expanded in x around inf 92.2%

      \[\leadsto \frac{60}{\color{blue}{\frac{z - t}{x}}} + a \cdot 120 \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+94} \lor \neg \left(y \leq 3.2 \cdot 10^{-10}\right):\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+92}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-10}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -9e+92)
   (+ (* a 120.0) (/ (* y -60.0) (- z t)))
   (if (<= y 2.8e-10)
     (+ (* a 120.0) (/ (* 60.0 x) (- z t)))
     (+ (* a 120.0) (* y (/ -60.0 (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -9e+92) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else if (y <= 2.8e-10) {
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	} else {
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (y <= (-9d+92)) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    else if (y <= 2.8d-10) then
        tmp = (a * 120.0d0) + ((60.0d0 * x) / (z - t))
    else
        tmp = (a * 120.0d0) + (y * ((-60.0d0) / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -9e+92) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else if (y <= 2.8e-10) {
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	} else {
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -9e+92:
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	elif y <= 2.8e-10:
		tmp = (a * 120.0) + ((60.0 * x) / (z - t))
	else:
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -9e+92)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	elseif (y <= 2.8e-10)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(-60.0 / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -9e+92)
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	elseif (y <= 2.8e-10)
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	else
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -9e+92], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-10], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.9999999999999998e92

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 94.0%

      \[\leadsto \frac{\color{blue}{-60 \cdot y}}{z - t} + a \cdot 120 \]

   if -8.9999999999999998e92 < y < 2.80000000000000015e-10

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 92.2%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} + a \cdot 120 \]
   6. Step-by-step derivation

      1. associate-*r/ 92.2%

         \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} + a \cdot 120 \]

   7. Simplified 92.2%

      \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} + a \cdot 120 \]

   if 2.80000000000000015e-10 < y

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 85.4%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} + a \cdot 120 \]
   6. Step-by-step derivation

      1. associate-*r/ 85.4%

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} + a \cdot 120 \]

      2. *-commutative 85.4%

         \[\leadsto \frac{\color{blue}{y \cdot -60}}{z - t} + a \cdot 120 \]

      3. *-lft-identity 85.4%

         \[\leadsto \frac{y \cdot -60}{\color{blue}{1 \cdot \left(z - t\right)}} + a \cdot 120 \]

      4. times-frac 85.4%

         \[\leadsto \color{blue}{\frac{y}{1} \cdot \frac{-60}{z - t}} + a \cdot 120 \]

      5. /-rgt-identity 85.4%

         \[\leadsto \color{blue}{y} \cdot \frac{-60}{z - t} + a \cdot 120 \]

   7. Simplified 85.4%

      \[\leadsto \color{blue}{y \cdot \frac{-60}{z - t}} + a \cdot 120 \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+92}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-10}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+93}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-10}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6.2e+93)
   (+ (* a 120.0) (/ (* y -60.0) (- z t)))
   (if (<= y 3.2e-10)
     (+ (* a 120.0) (/ 60.0 (/ (- z t) x)))
     (+ (* a 120.0) (* y (/ -60.0 (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6.2e+93) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else if (y <= 3.2e-10) {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	} else {
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (y <= (-6.2d+93)) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    else if (y <= 3.2d-10) then
        tmp = (a * 120.0d0) + (60.0d0 / ((z - t) / x))
    else
        tmp = (a * 120.0d0) + (y * ((-60.0d0) / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6.2e+93) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else if (y <= 3.2e-10) {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	} else {
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -6.2e+93:
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	elif y <= 3.2e-10:
		tmp = (a * 120.0) + (60.0 / ((z - t) / x))
	else:
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -6.2e+93)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	elseif (y <= 3.2e-10)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(z - t) / x)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(-60.0 / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -6.2e+93)
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	elseif (y <= 3.2e-10)
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	else
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -6.2e+93], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-10], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.20000000000000038e93

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 94.0%

      \[\leadsto \frac{\color{blue}{-60 \cdot y}}{z - t} + a \cdot 120 \]

   if -6.20000000000000038e93 < y < 3.19999999999999981e-10

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.7%

         \[\leadsto 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}} + a \cdot 120 \]

      2. un-div-inv 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   7. Taylor expanded in x around inf 92.2%

      \[\leadsto \frac{60}{\color{blue}{\frac{z - t}{x}}} + a \cdot 120 \]

   if 3.19999999999999981e-10 < y

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 85.4%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} + a \cdot 120 \]
   6. Step-by-step derivation

      1. associate-*r/ 85.4%

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} + a \cdot 120 \]

      2. *-commutative 85.4%

         \[\leadsto \frac{\color{blue}{y \cdot -60}}{z - t} + a \cdot 120 \]

      3. *-lft-identity 85.4%

         \[\leadsto \frac{y \cdot -60}{\color{blue}{1 \cdot \left(z - t\right)}} + a \cdot 120 \]

      4. times-frac 85.4%

         \[\leadsto \color{blue}{\frac{y}{1} \cdot \frac{-60}{z - t}} + a \cdot 120 \]

      5. /-rgt-identity 85.4%

         \[\leadsto \color{blue}{y} \cdot \frac{-60}{z - t} + a \cdot 120 \]

   7. Simplified 85.4%

      \[\leadsto \color{blue}{y \cdot \frac{-60}{z - t}} + a \cdot 120 \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+93}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-10}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 77.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+32}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+68}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.5e+32)
   (+ (* a 120.0) (/ 60.0 (/ z x)))
   (if (<= z 1.3e+68)
     (+ (* a 120.0) (* -60.0 (/ (- x y) t)))
     (+ (* a 120.0) (/ (* y -60.0) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+32) {
		tmp = (a * 120.0) + (60.0 / (z / x));
	} else if (z <= 1.3e+68) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (z <= (-1.5d+32)) then
        tmp = (a * 120.0d0) + (60.0d0 / (z / x))
    else if (z <= 1.3d+68) then
        tmp = (a * 120.0d0) + ((-60.0d0) * ((x - y) / t))
    else
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+32) {
		tmp = (a * 120.0) + (60.0 / (z / x));
	} else if (z <= 1.3e+68) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.5e+32:
		tmp = (a * 120.0) + (60.0 / (z / x))
	elif z <= 1.3e+68:
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t))
	else:
		tmp = (a * 120.0) + ((y * -60.0) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.5e+32)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(z / x)));
	elseif (z <= 1.3e+68)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(Float64(x - y) / t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.5e+32)
		tmp = (a * 120.0) + (60.0 / (z / x));
	elseif (z <= 1.3e+68)
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	else
		tmp = (a * 120.0) + ((y * -60.0) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.5e+32], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+68], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5e32

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.7%

         \[\leadsto 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}} + a \cdot 120 \]

      2. un-div-inv 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   7. Taylor expanded in x around inf 83.6%

      \[\leadsto \frac{60}{\color{blue}{\frac{z - t}{x}}} + a \cdot 120 \]

   8. Taylor expanded in z around inf 75.8%

      \[\leadsto \frac{60}{\color{blue}{\frac{z}{x}}} + a \cdot 120 \]

   if -1.5e32 < z < 1.2999999999999999e68

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 82.8%

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t}} + a \cdot 120 \]

   if 1.2999999999999999e68 < z

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 86.8%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} + a \cdot 120 \]
   6. Step-by-step derivation

      1. associate-*r/ 86.9%

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} + a \cdot 120 \]

      2. *-commutative 86.9%

         \[\leadsto \frac{\color{blue}{y \cdot -60}}{z - t} + a \cdot 120 \]

      3. *-lft-identity 86.9%

         \[\leadsto \frac{y \cdot -60}{\color{blue}{1 \cdot \left(z - t\right)}} + a \cdot 120 \]

      4. times-frac 86.8%

         \[\leadsto \color{blue}{\frac{y}{1} \cdot \frac{-60}{z - t}} + a \cdot 120 \]

      5. /-rgt-identity 86.8%

         \[\leadsto \color{blue}{y} \cdot \frac{-60}{z - t} + a \cdot 120 \]

   7. Simplified 86.8%

      \[\leadsto \color{blue}{y \cdot \frac{-60}{z - t}} + a \cdot 120 \]

   8. Taylor expanded in z around inf 84.7%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z}} + a \cdot 120 \]
   9. Step-by-step derivation

      1. associate-*r/ 84.8%

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z}} + a \cdot 120 \]

   10. Applied egg-rr 84.8%

       \[\leadsto \color{blue}{\frac{-60 \cdot y}{z}} + a \cdot 120 \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+32}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+68}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-94}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-135}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-85}:\\ \;\;\;\;\frac{-60}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.2e-94)
   (* a 120.0)
   (if (<= a 4.5e-135)
     (* 60.0 (/ x (- z t)))
     (if (<= a 1.7e-85) (/ -60.0 (/ z y)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e-94) {
		tmp = a * 120.0;
	} else if (a <= 4.5e-135) {
		tmp = 60.0 * (x / (z - t));
	} else if (a <= 1.7e-85) {
		tmp = -60.0 / (z / y);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (a <= (-3.2d-94)) then
        tmp = a * 120.0d0
    else if (a <= 4.5d-135) then
        tmp = 60.0d0 * (x / (z - t))
    else if (a <= 1.7d-85) then
        tmp = (-60.0d0) / (z / y)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e-94) {
		tmp = a * 120.0;
	} else if (a <= 4.5e-135) {
		tmp = 60.0 * (x / (z - t));
	} else if (a <= 1.7e-85) {
		tmp = -60.0 / (z / y);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.2e-94:
		tmp = a * 120.0
	elif a <= 4.5e-135:
		tmp = 60.0 * (x / (z - t))
	elif a <= 1.7e-85:
		tmp = -60.0 / (z / y)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.2e-94)
		tmp = Float64(a * 120.0);
	elseif (a <= 4.5e-135)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	elseif (a <= 1.7e-85)
		tmp = Float64(-60.0 / Float64(z / y));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.2e-94)
		tmp = a * 120.0;
	elseif (a <= 4.5e-135)
		tmp = 60.0 * (x / (z - t));
	elseif (a <= 1.7e-85)
		tmp = -60.0 / (z / y);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.2e-94], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 4.5e-135], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e-85], N[(-60.0 / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.19999999999999997e-94 or 1.7e-85 < a

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} + a \cdot 120 \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{60}{z - t}, a \cdot 120\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{z + \left(-t\right)}}, a \cdot 120\right) \]

      5. +-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(-t\right) + z}}, a \cdot 120\right) \]

      6. neg-sub0 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(0 - t\right)} + z}, a \cdot 120\right) \]

      7. associate-+l- 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{0 - \left(t - z\right)}}, a \cdot 120\right) \]

      8. sub0-neg 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{-\left(t - z\right)}}, a \cdot 120\right) \]

      9. distribute-frac-neg2 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{-\frac{60}{t - z}}, a \cdot 120\right) \]

      10. distribute-neg-frac 99.8%

          \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{\frac{-60}{t - z}}, a \cdot 120\right) \]

      11. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x - y, \frac{\color{blue}{-60}}{t - z}, a \cdot 120\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{-60}{t - z}, a \cdot 120\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 65.9%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -3.19999999999999997e-94 < a < 4.49999999999999987e-135

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{a \cdot 120 + 60 \cdot \frac{x - y}{z - t}} \]

      2. fma-define 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, 60 \cdot \frac{x - y}{z - t}\right)} \]

      3. clear-num 99.5%

         \[\leadsto \mathsf{fma}\left(a, 120, 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}}\right) \]

      4. un-div-inv 99.7%

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{\frac{z - t}{x - y}}}\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)} \]

   7. Taylor expanded in x around inf 49.8%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]

   if 4.49999999999999987e-135 < a < 1.7e-85

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.4%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 99.4%

         \[\leadsto \color{blue}{a \cdot 120 + 60 \cdot \frac{x - y}{z - t}} \]

      2. fma-define 99.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, 60 \cdot \frac{x - y}{z - t}\right)} \]

      3. clear-num 99.7%

         \[\leadsto \mathsf{fma}\left(a, 120, 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}}\right) \]

      4. un-div-inv 99.9%

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{\frac{z - t}{x - y}}}\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)} \]

   7. Taylor expanded in a around 0 81.8%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 82.0%

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      2. associate-*l/ 82.0%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} \]

      3. metadata-eval 82.0%

         \[\leadsto \frac{\color{blue}{60 \cdot 1}}{z - t} \cdot \left(x - y\right) \]

      4. associate-*r/ 82.2%

         \[\leadsto \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)} \cdot \left(x - y\right) \]

      5. *-commutative 82.2%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      6. associate-*r/ 82.0%

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{60 \cdot 1}{z - t}} \]

      7. metadata-eval 82.0%

         \[\leadsto \left(x - y\right) \cdot \frac{\color{blue}{60}}{z - t} \]

   9. Simplified 82.0%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} \]

   10. Taylor expanded in z around inf 65.1%

       \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{60}{z}} \]

   11. Taylor expanded in x around 0 56.4%

       \[\leadsto \color{blue}{-60 \cdot \frac{y}{z}} \]
   12. Step-by-step derivation

       1. associate-*r/ 56.4%

          \[\leadsto \color{blue}{\frac{-60 \cdot y}{z}} \]

       2. remove-double-neg 56.4%

          \[\leadsto \frac{-60 \cdot y}{\color{blue}{-\left(-z\right)}} \]

       3. distribute-neg-frac2 56.4%

          \[\leadsto \color{blue}{-\frac{-60 \cdot y}{-z}} \]

       4. distribute-frac-neg 56.4%

          \[\leadsto \color{blue}{\frac{--60 \cdot y}{-z}} \]

       5. distribute-frac-neg2 56.4%

          \[\leadsto \color{blue}{-\frac{--60 \cdot y}{z}} \]

       6. distribute-neg-frac 56.4%

          \[\leadsto \color{blue}{\frac{-\left(--60 \cdot y\right)}{z}} \]

       7. *-commutative 56.4%

          \[\leadsto \frac{-\left(-\color{blue}{y \cdot -60}\right)}{z} \]

       8. distribute-rgt-neg-in 56.4%

          \[\leadsto \frac{-\color{blue}{y \cdot \left(--60\right)}}{z} \]

       9. metadata-eval 56.4%

          \[\leadsto \frac{-y \cdot \color{blue}{60}}{z} \]

       10. distribute-lft-neg-out 56.4%

           \[\leadsto \frac{\color{blue}{\left(-y\right) \cdot 60}}{z} \]

       11. associate-*r/ 56.6%

           \[\leadsto \color{blue}{\left(-y\right) \cdot \frac{60}{z}} \]

       12. *-commutative 56.6%

           \[\leadsto \color{blue}{\frac{60}{z} \cdot \left(-y\right)} \]

       13. distribute-rgt-neg-out 56.6%

           \[\leadsto \color{blue}{-\frac{60}{z} \cdot y} \]

       14. distribute-lft-neg-in 56.6%

           \[\leadsto \color{blue}{\left(-\frac{60}{z}\right) \cdot y} \]

       15. distribute-neg-frac 56.6%

           \[\leadsto \color{blue}{\frac{-60}{z}} \cdot y \]

       16. metadata-eval 56.6%

           \[\leadsto \frac{\color{blue}{-60}}{z} \cdot y \]

       17. associate-/r/ 56.6%

           \[\leadsto \color{blue}{\frac{-60}{\frac{z}{y}}} \]

   13. Simplified 56.6%

       \[\leadsto \color{blue}{\frac{-60}{\frac{z}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-94}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-135}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-85}:\\ \;\;\;\;\frac{-60}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 75.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -20.5 \lor \neg \left(a \leq 4.9 \cdot 10^{+30}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -20.5) (not (<= a 4.9e+30)))
   (* a 120.0)
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -20.5) || !(a <= 4.9e+30)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((a <= (-20.5d0)) .or. (.not. (a <= 4.9d+30))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -20.5) || !(a <= 4.9e+30)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -20.5) or not (a <= 4.9e+30):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -20.5) || !(a <= 4.9e+30))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -20.5) || ~((a <= 4.9e+30)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -20.5], N[Not[LessEqual[a, 4.9e+30]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -20.5 or 4.89999999999999984e30 < a

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} + a \cdot 120 \]

      3. fma-define 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{60}{z - t}, a \cdot 120\right)} \]

      4. sub-neg 99.9%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{z + \left(-t\right)}}, a \cdot 120\right) \]

      5. +-commutative 99.9%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(-t\right) + z}}, a \cdot 120\right) \]

      6. neg-sub0 99.9%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(0 - t\right)} + z}, a \cdot 120\right) \]

      7. associate-+l- 99.9%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{0 - \left(t - z\right)}}, a \cdot 120\right) \]

      8. sub0-neg 99.9%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{-\left(t - z\right)}}, a \cdot 120\right) \]

      9. distribute-frac-neg2 99.9%

         \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{-\frac{60}{t - z}}, a \cdot 120\right) \]

      10. distribute-neg-frac 99.9%

          \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{\frac{-60}{t - z}}, a \cdot 120\right) \]

      11. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(x - y, \frac{\color{blue}{-60}}{t - z}, a \cdot 120\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{-60}{t - z}, a \cdot 120\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 73.7%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -20.5 < a < 4.89999999999999984e30

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 77.7%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -20.5 \lor \neg \left(a \leq 4.9 \cdot 10^{+30}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z - t} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (* a 120.0) (* (- x y) (/ 60.0 (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	return (a * 120.0) + ((x - y) * (60.0 / (z - t)));
}

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = (a * 120.0d0) + ((x - y) * (60.0d0 / (z - t)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (a * 120.0) + ((x - y) * (60.0 / (z - t)));
}

Python

def code(x, y, z, t, a):
	return (a * 120.0) + ((x - y) * (60.0 / (z - t)))

Julia

function code(x, y, z, t, a)
	return Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(60.0 / Float64(z - t))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (a * 120.0) + ((x - y) * (60.0 / (z - t)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Add Preprocessing
3. Step-by-step derivation

   1. *-commutative 99.8%

      \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

   2. associate-/l* 99.8%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} + a \cdot 120 \]

4. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} + a \cdot 120 \]

5. Final simplification 99.8%

   \[\leadsto a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z - t} \]
6. Add Preprocessing

Alternative 16: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ a \cdot 120 + 60 \cdot \frac{x - y}{z - t} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (* a 120.0) (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	return (a * 120.0) + (60.0 * ((x - y) / (z - t)));
}

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = (a * 120.0d0) + (60.0d0 * ((x - y) / (z - t)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (a * 120.0) + (60.0 * ((x - y) / (z - t)));
}

Python

def code(x, y, z, t, a):
	return (a * 120.0) + (60.0 * ((x - y) / (z - t)))

Julia

function code(x, y, z, t, a)
	return Float64(Float64(a * 120.0) + Float64(60.0 * Float64(Float64(x - y) / Float64(z - t))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (a * 120.0) + (60.0 * ((x - y) / (z - t)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Step-by-step derivation

   1. associate-/l* 99.7%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

3. Simplified 99.7%

   \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
4. Add Preprocessing

5. Final simplification 99.7%

   \[\leadsto a \cdot 120 + 60 \cdot \frac{x - y}{z - t} \]
6. Add Preprocessing

Alternative 17: 51.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 7.6 \cdot 10^{+205}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x 7.6e+205) (* a 120.0) (/ -60.0 (/ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 7.6e+205) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / (t / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (x <= 7.6d+205) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) / (t / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 7.6e+205) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / (t / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 7.6e+205:
		tmp = a * 120.0
	else:
		tmp = -60.0 / (t / x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= 7.6e+205)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 / Float64(t / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= 7.6e+205)
		tmp = a * 120.0;
	else
		tmp = -60.0 / (t / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, 7.6e+205], N[(a * 120.0), $MachinePrecision], N[(-60.0 / N[(t / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 7.6000000000000001e205

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.8%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} + a \cdot 120 \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{60}{z - t}, a \cdot 120\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{z + \left(-t\right)}}, a \cdot 120\right) \]

      5. +-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(-t\right) + z}}, a \cdot 120\right) \]

      6. neg-sub0 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(0 - t\right)} + z}, a \cdot 120\right) \]

      7. associate-+l- 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{0 - \left(t - z\right)}}, a \cdot 120\right) \]

      8. sub0-neg 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{-\left(t - z\right)}}, a \cdot 120\right) \]

      9. distribute-frac-neg2 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{-\frac{60}{t - z}}, a \cdot 120\right) \]

      10. distribute-neg-frac 99.8%

          \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{\frac{-60}{t - z}}, a \cdot 120\right) \]

      11. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x - y, \frac{\color{blue}{-60}}{t - z}, a \cdot 120\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{-60}{t - z}, a \cdot 120\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 50.0%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if 7.6000000000000001e205 < x

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{a \cdot 120 + 60 \cdot \frac{x - y}{z - t}} \]

      2. fma-define 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, 60 \cdot \frac{x - y}{z - t}\right)} \]

      3. clear-num 99.6%

         \[\leadsto \mathsf{fma}\left(a, 120, 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}}\right) \]

      4. un-div-inv 99.9%

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{\frac{z - t}{x - y}}}\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)} \]

   7. Taylor expanded in x around inf 84.9%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]

   8. Taylor expanded in z around 0 56.6%

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t}} \]
   9. Step-by-step derivation

      1. clear-num 56.6%

         \[\leadsto -60 \cdot \color{blue}{\frac{1}{\frac{t}{x}}} \]

      2. un-div-inv 56.7%

         \[\leadsto \color{blue}{\frac{-60}{\frac{t}{x}}} \]

   10. Applied egg-rr 56.7%

       \[\leadsto \color{blue}{\frac{-60}{\frac{t}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7.6 \cdot 10^{+205}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 51.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5.3 \cdot 10^{+191}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x 5.3e+191) (* a 120.0) (* x (/ -60.0 t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 5.3e+191) {
		tmp = a * 120.0;
	} else {
		tmp = x * (-60.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (x <= 5.3d+191) then
        tmp = a * 120.0d0
    else
        tmp = x * ((-60.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 5.3e+191) {
		tmp = a * 120.0;
	} else {
		tmp = x * (-60.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 5.3e+191:
		tmp = a * 120.0
	else:
		tmp = x * (-60.0 / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= 5.3e+191)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(x * Float64(-60.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= 5.3e+191)
		tmp = a * 120.0;
	else
		tmp = x * (-60.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, 5.3e+191], N[(a * 120.0), $MachinePrecision], N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.30000000000000031e191

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.8%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} + a \cdot 120 \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{60}{z - t}, a \cdot 120\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{z + \left(-t\right)}}, a \cdot 120\right) \]

      5. +-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(-t\right) + z}}, a \cdot 120\right) \]

      6. neg-sub0 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(0 - t\right)} + z}, a \cdot 120\right) \]

      7. associate-+l- 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{0 - \left(t - z\right)}}, a \cdot 120\right) \]

      8. sub0-neg 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{-\left(t - z\right)}}, a \cdot 120\right) \]

      9. distribute-frac-neg2 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{-\frac{60}{t - z}}, a \cdot 120\right) \]

      10. distribute-neg-frac 99.8%

          \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{\frac{-60}{t - z}}, a \cdot 120\right) \]

      11. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x - y, \frac{\color{blue}{-60}}{t - z}, a \cdot 120\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{-60}{t - z}, a \cdot 120\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 50.0%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if 5.30000000000000031e191 < x

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{a \cdot 120 + 60 \cdot \frac{x - y}{z - t}} \]

      2. fma-define 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, 60 \cdot \frac{x - y}{z - t}\right)} \]

      3. clear-num 99.6%

         \[\leadsto \mathsf{fma}\left(a, 120, 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}}\right) \]

      4. un-div-inv 99.9%

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{\frac{z - t}{x - y}}}\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)} \]

   7. Taylor expanded in x around inf 84.9%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]

   8. Taylor expanded in z around 0 56.6%

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t}} \]
   9. Step-by-step derivation

      1. clear-num 56.6%

         \[\leadsto -60 \cdot \color{blue}{\frac{1}{\frac{t}{x}}} \]

      2. un-div-inv 56.7%

         \[\leadsto \color{blue}{\frac{-60}{\frac{t}{x}}} \]

   10. Applied egg-rr 56.7%

       \[\leadsto \color{blue}{\frac{-60}{\frac{t}{x}}} \]
   11. Step-by-step derivation

       1. associate-/r/ 56.6%

          \[\leadsto \color{blue}{\frac{-60}{t} \cdot x} \]

   12. Simplified 56.6%

       \[\leadsto \color{blue}{\frac{-60}{t} \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.3 \cdot 10^{+191}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 51.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.3 \cdot 10^{+206}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x 2.3e+206) (* a 120.0) (* -60.0 (/ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 2.3e+206) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (x <= 2.3d+206) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 2.3e+206) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 2.3e+206:
		tmp = a * 120.0
	else:
		tmp = -60.0 * (x / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= 2.3e+206)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= 2.3e+206)
		tmp = a * 120.0;
	else
		tmp = -60.0 * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, 2.3e+206], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.30000000000000016e206

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

      2. associate-/l* 99.8%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} + a \cdot 120 \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{60}{z - t}, a \cdot 120\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{z + \left(-t\right)}}, a \cdot 120\right) \]

      5. +-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(-t\right) + z}}, a \cdot 120\right) \]

      6. neg-sub0 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(0 - t\right)} + z}, a \cdot 120\right) \]

      7. associate-+l- 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{0 - \left(t - z\right)}}, a \cdot 120\right) \]

      8. sub0-neg 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{-\left(t - z\right)}}, a \cdot 120\right) \]

      9. distribute-frac-neg2 99.8%

         \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{-\frac{60}{t - z}}, a \cdot 120\right) \]

      10. distribute-neg-frac 99.8%

          \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{\frac{-60}{t - z}}, a \cdot 120\right) \]

      11. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x - y, \frac{\color{blue}{-60}}{t - z}, a \cdot 120\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{-60}{t - z}, a \cdot 120\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 50.0%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if 2.30000000000000016e206 < x

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{a \cdot 120 + 60 \cdot \frac{x - y}{z - t}} \]

      2. fma-define 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, 60 \cdot \frac{x - y}{z - t}\right)} \]

      3. clear-num 99.6%

         \[\leadsto \mathsf{fma}\left(a, 120, 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}}\right) \]

      4. un-div-inv 99.9%

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{\frac{z - t}{x - y}}}\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)} \]

   7. Taylor expanded in x around inf 84.9%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]

   8. Taylor expanded in z around 0 56.6%

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.3 \cdot 10^{+206}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 50.6% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* a 120.0))

C

double code(double x, double y, double z, double t, double a) {
	return a * 120.0;
}

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = a * 120.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return a * 120.0;
}

Python

def code(x, y, z, t, a):
	return a * 120.0

Julia

function code(x, y, z, t, a)
	return Float64(a * 120.0)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = a * 120.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(a * 120.0), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Step-by-step derivation

   1. *-commutative 99.8%

      \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]

   2. associate-/l* 99.8%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} + a \cdot 120 \]

   3. fma-define 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{60}{z - t}, a \cdot 120\right)} \]

   4. sub-neg 99.8%

      \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{z + \left(-t\right)}}, a \cdot 120\right) \]

   5. +-commutative 99.8%

      \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(-t\right) + z}}, a \cdot 120\right) \]

   6. neg-sub0 99.8%

      \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{\left(0 - t\right)} + z}, a \cdot 120\right) \]

   7. associate-+l- 99.8%

      \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{0 - \left(t - z\right)}}, a \cdot 120\right) \]

   8. sub0-neg 99.8%

      \[\leadsto \mathsf{fma}\left(x - y, \frac{60}{\color{blue}{-\left(t - z\right)}}, a \cdot 120\right) \]

   9. distribute-frac-neg2 99.8%

      \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{-\frac{60}{t - z}}, a \cdot 120\right) \]

   10. distribute-neg-frac 99.8%

       \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{\frac{-60}{t - z}}, a \cdot 120\right) \]

   11. metadata-eval 99.8%

       \[\leadsto \mathsf{fma}\left(x - y, \frac{\color{blue}{-60}}{t - z}, a \cdot 120\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{-60}{t - z}, a \cdot 120\right)} \]
4. Add Preprocessing

5. Taylor expanded in t around inf 47.1%

   \[\leadsto \color{blue}{120 \cdot a} \]

6. Final simplification 47.1%

   \[\leadsto a \cdot 120 \]
7. Add Preprocessing

Developer Target 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{60}{\frac{z - t}{x - y}} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ 60.0 (/ (- z t) (- x y))) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = (60.0d0 / ((z - t) / (x - y))) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(60.0 / Float64(Float64(z - t) / Float64(x - y))) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (60.0 / ((z - t) / (x - y))) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024170 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (/ 60 (/ (- z t) (- x y))) (* a 120)))

  (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))