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

Percentage Accurate: 99.4% → 99.8%

Time: 14.1s

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: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.4%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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 99.8%

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

   3. clear-num 99.8%

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

   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. Add Preprocessing

Alternative 2: 83.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+163}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \frac{-60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -2e+163)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= t_1 5e+75) (+ (* y (/ -60.0 (- z t))) (* a 120.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+163) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (t_1 <= 5e+75) {
		tmp = (y * (-60.0 / (z - t))) + (a * 120.0);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-2d+163)) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if (t_1 <= 5d+75) then
        tmp = (y * ((-60.0d0) / (z - t))) + (a * 120.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+163) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (t_1 <= 5e+75) {
		tmp = (y * (-60.0 / (z - t))) + (a * 120.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -2e+163:
		tmp = 60.0 * ((x - y) / (z - t))
	elif t_1 <= 5e+75:
		tmp = (y * (-60.0 / (z - t))) + (a * 120.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+163)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (t_1 <= 5e+75)
		tmp = Float64(Float64(y * Float64(-60.0 / Float64(z - t))) + Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+163)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif (t_1 <= 5e+75)
		tmp = (y * (-60.0 / (z - t))) + (a * 120.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+163], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+75], N[(N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.9999999999999999e163

   1. Initial program 97.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 a around 0 91.0%

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

   if -1.9999999999999999e163 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.0000000000000002e75

   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 0 86.1%

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

      1. associate-*r/ 86.1%

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

      2. *-commutative 86.1%

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

      3. *-lft-identity 86.1%

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

      4. times-frac 86.1%

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

      5. /-rgt-identity 86.1%

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

   7. Simplified 86.1%

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

   if 5.0000000000000002e75 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   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* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around 0 93.0%

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

      1. associate-*r/ 93.2%

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

   7. Applied egg-rr 93.2%

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

Alternative 3: 58.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -150:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-256}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-199}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -150.0)
   (* a 120.0)
   (if (<= a -1.95e-256)
     (* -60.0 (/ (- x y) t))
     (if (<= a 1.7e-199)
       (* x (/ 60.0 (- z t)))
       (if (<= a 9.2e-79) (* 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 <= -150.0) {
		tmp = a * 120.0;
	} else if (a <= -1.95e-256) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= 1.7e-199) {
		tmp = x * (60.0 / (z - t));
	} else if (a <= 9.2e-79) {
		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 <= (-150.0d0)) then
        tmp = a * 120.0d0
    else if (a <= (-1.95d-256)) then
        tmp = (-60.0d0) * ((x - y) / t)
    else if (a <= 1.7d-199) then
        tmp = x * (60.0d0 / (z - t))
    else if (a <= 9.2d-79) 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 <= -150.0) {
		tmp = a * 120.0;
	} else if (a <= -1.95e-256) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= 1.7e-199) {
		tmp = x * (60.0 / (z - t));
	} else if (a <= 9.2e-79) {
		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 <= -150.0:
		tmp = a * 120.0
	elif a <= -1.95e-256:
		tmp = -60.0 * ((x - y) / t)
	elif a <= 1.7e-199:
		tmp = x * (60.0 / (z - t))
	elif a <= 9.2e-79:
		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 <= -150.0)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.95e-256)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	elseif (a <= 1.7e-199)
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	elseif (a <= 9.2e-79)
		tmp = Float64(y * Float64(-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 <= -150.0)
		tmp = a * 120.0;
	elseif (a <= -1.95e-256)
		tmp = -60.0 * ((x - y) / t);
	elseif (a <= 1.7e-199)
		tmp = x * (60.0 / (z - t));
	elseif (a <= 9.2e-79)
		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, -150.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.95e-256], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e-199], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.2e-79], N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -150 or 9.20000000000000047e-79 < 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* 99.8%

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

      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 76.8%

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

   if -150 < a < -1.9499999999999999e-256

   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 76.4%

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

   6. Taylor expanded in z around 0 55.2%

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

   if -1.9499999999999999e-256 < a < 1.70000000000000003e-199

   1. Initial program 96.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf 68.2%

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

      1. associate-*r/ 68.3%

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

      2. associate-*l/ 68.3%

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

      3. *-commutative 68.3%

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

   9. Simplified 68.3%

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

   if 1.70000000000000003e-199 < a < 9.20000000000000047e-79

   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* 99.7%

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

   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 99.7%

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

      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 y around inf 62.2%

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

      1. associate-*r/ 62.2%

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

      2. *-commutative 62.2%

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

      3. associate-/l* 62.5%

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

   9. Simplified 62.5%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -150:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-256}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-199}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -230:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.32 \cdot 10^{-256}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-79}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -230.0)
   (* a 120.0)
   (if (<= a -1.32e-256)
     (* -60.0 (/ (- x y) t))
     (if (<= a 7.5e-201)
       (* x (/ 60.0 (- z t)))
       (if (<= a 5.1e-79) (* 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 <= -230.0) {
		tmp = a * 120.0;
	} else if (a <= -1.32e-256) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= 7.5e-201) {
		tmp = x * (60.0 / (z - t));
	} else if (a <= 5.1e-79) {
		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 <= (-230.0d0)) then
        tmp = a * 120.0d0
    else if (a <= (-1.32d-256)) then
        tmp = (-60.0d0) * ((x - y) / t)
    else if (a <= 7.5d-201) then
        tmp = x * (60.0d0 / (z - t))
    else if (a <= 5.1d-79) 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 <= -230.0) {
		tmp = a * 120.0;
	} else if (a <= -1.32e-256) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= 7.5e-201) {
		tmp = x * (60.0 / (z - t));
	} else if (a <= 5.1e-79) {
		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 <= -230.0:
		tmp = a * 120.0
	elif a <= -1.32e-256:
		tmp = -60.0 * ((x - y) / t)
	elif a <= 7.5e-201:
		tmp = x * (60.0 / (z - t))
	elif a <= 5.1e-79:
		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 <= -230.0)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.32e-256)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	elseif (a <= 7.5e-201)
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	elseif (a <= 5.1e-79)
		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 <= -230.0)
		tmp = a * 120.0;
	elseif (a <= -1.32e-256)
		tmp = -60.0 * ((x - y) / t);
	elseif (a <= 7.5e-201)
		tmp = x * (60.0 / (z - t));
	elseif (a <= 5.1e-79)
		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, -230.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.32e-256], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-201], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.1e-79], 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 < -230 or 5.0999999999999999e-79 < 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* 99.8%

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

      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 76.8%

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

   if -230 < a < -1.32e-256

   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 76.4%

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

   6. Taylor expanded in z around 0 55.2%

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

   if -1.32e-256 < a < 7.49999999999999987e-201

   1. Initial program 96.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf 68.2%

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

      1. associate-*r/ 68.3%

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

      2. associate-*l/ 68.3%

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

      3. *-commutative 68.3%

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

   9. Simplified 68.3%

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

   if 7.49999999999999987e-201 < a < 5.0999999999999999e-79

   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* 99.9%

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

      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 y around inf 62.2%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -230:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.32 \cdot 10^{-256}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-79}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -11500:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8.1 \cdot 10^{-258}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-199}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-78}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -11500.0)
   (* a 120.0)
   (if (<= a -8.1e-258)
     (* -60.0 (/ (- x y) t))
     (if (<= a 7.5e-199)
       (* 60.0 (/ x (- z t)))
       (if (<= a 5.8e-78) (* 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 <= -11500.0) {
		tmp = a * 120.0;
	} else if (a <= -8.1e-258) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= 7.5e-199) {
		tmp = 60.0 * (x / (z - t));
	} else if (a <= 5.8e-78) {
		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 <= (-11500.0d0)) then
        tmp = a * 120.0d0
    else if (a <= (-8.1d-258)) then
        tmp = (-60.0d0) * ((x - y) / t)
    else if (a <= 7.5d-199) then
        tmp = 60.0d0 * (x / (z - t))
    else if (a <= 5.8d-78) 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 <= -11500.0) {
		tmp = a * 120.0;
	} else if (a <= -8.1e-258) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= 7.5e-199) {
		tmp = 60.0 * (x / (z - t));
	} else if (a <= 5.8e-78) {
		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 <= -11500.0:
		tmp = a * 120.0
	elif a <= -8.1e-258:
		tmp = -60.0 * ((x - y) / t)
	elif a <= 7.5e-199:
		tmp = 60.0 * (x / (z - t))
	elif a <= 5.8e-78:
		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 <= -11500.0)
		tmp = Float64(a * 120.0);
	elseif (a <= -8.1e-258)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	elseif (a <= 7.5e-199)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	elseif (a <= 5.8e-78)
		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 <= -11500.0)
		tmp = a * 120.0;
	elseif (a <= -8.1e-258)
		tmp = -60.0 * ((x - y) / t);
	elseif (a <= 7.5e-199)
		tmp = 60.0 * (x / (z - t));
	elseif (a <= 5.8e-78)
		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, -11500.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -8.1e-258], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-199], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e-78], 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 < -11500 or 5.8000000000000001e-78 < 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* 99.8%

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

      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 76.8%

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

   if -11500 < a < -8.1000000000000003e-258

   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 76.4%

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

   6. Taylor expanded in z around 0 55.2%

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

   if -8.1000000000000003e-258 < a < 7.5000000000000003e-199

   1. Initial program 96.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf 68.2%

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

   if 7.5000000000000003e-199 < a < 5.8000000000000001e-78

   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* 99.9%

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

      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 y around inf 62.2%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -11500:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8.1 \cdot 10^{-258}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-199}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-78}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -20000000 \lor \neg \left(a \cdot 120 \leq 10^{-76}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -20000000.0) (not (<= (* a 120.0) 1e-76)))
   (* 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 * 120.0) <= -20000000.0) || !((a * 120.0) <= 1e-76)) {
		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 * 120.0d0) <= (-20000000.0d0)) .or. (.not. ((a * 120.0d0) <= 1d-76))) 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 * 120.0) <= -20000000.0) || !((a * 120.0) <= 1e-76)) {
		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 * 120.0) <= -20000000.0) or not ((a * 120.0) <= 1e-76):
		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 ((Float64(a * 120.0) <= -20000000.0) || !(Float64(a * 120.0) <= 1e-76))
		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 * 120.0) <= -20000000.0) || ~(((a * 120.0) <= 1e-76)))
		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[N[(a * 120.0), $MachinePrecision], -20000000.0], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-76]], $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 (*.f64 a #s(literal 120 binary64)) < -2e7 or 9.99999999999999927e-77 < (*.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* 99.8%

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

      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 76.8%

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

   if -2e7 < (*.f64 a #s(literal 120 binary64)) < 9.99999999999999927e-77

   1. Initial program 98.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in a around 0 84.0%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -20000000 \lor \neg \left(a \cdot 120 \leq 10^{-76}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -20000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-76}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -20000000.0)
   (* a 120.0)
   (if (<= (* a 120.0) 1e-76)
     (/ 60.0 (/ (- z t) (- x y)))
     (+ (* a 120.0) (/ (* 60.0 x) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -20000000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-76) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = (a * 120.0) + ((60.0 * x) / 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 ((a * 120.0d0) <= (-20000000.0d0)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-76) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else
        tmp = (a * 120.0d0) + ((60.0d0 * x) / 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 ((a * 120.0) <= -20000000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-76) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -20000000.0:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-76:
		tmp = 60.0 / ((z - t) / (x - y))
	else:
		tmp = (a * 120.0) + ((60.0 * x) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -20000000.0)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-76)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -20000000.0)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-76)
		tmp = 60.0 / ((z - t) / (x - y));
	else
		tmp = (a * 120.0) + ((60.0 * x) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -20000000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-76], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -2e7

   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 78.3%

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

   if -2e7 < (*.f64 a #s(literal 120 binary64)) < 9.99999999999999927e-77

   1. Initial program 98.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in a around 0 84.0%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.8%

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

   7. Applied egg-rr 84.1%

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

   if 9.99999999999999927e-77 < (*.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 inf 92.2%

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

      1. associate-*r/ 92.3%

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

   7. Simplified 92.3%

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

   8. Taylor expanded in z around inf 82.7%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -20000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-76}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -20000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-76}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -20000000.0)
   (* a 120.0)
   (if (<= (* a 120.0) 1e-76)
     (* 60.0 (/ (- x y) (- z t)))
     (+ (* a 120.0) (/ (* 60.0 x) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -20000000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-76) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + ((60.0 * x) / 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 ((a * 120.0d0) <= (-20000000.0d0)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-76) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (a * 120.0d0) + ((60.0d0 * x) / 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 ((a * 120.0) <= -20000000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-76) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -20000000.0:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-76:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (a * 120.0) + ((60.0 * x) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -20000000.0)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-76)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -20000000.0)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-76)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (a * 120.0) + ((60.0 * x) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -20000000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-76], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -2e7

   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 78.3%

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

   if -2e7 < (*.f64 a #s(literal 120 binary64)) < 9.99999999999999927e-77

   1. Initial program 98.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in a around 0 84.0%

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

   if 9.99999999999999927e-77 < (*.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 inf 92.2%

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

      1. associate-*r/ 92.3%

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

   7. Simplified 92.3%

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

   8. Taylor expanded in z around inf 82.7%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -20000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-76}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8500:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-258}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-101}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8500.0)
   (* a 120.0)
   (if (<= a -2.1e-258)
     (* -60.0 (/ (- x y) t))
     (if (<= a 1.08e-101) (* 60.0 (/ x (- z t))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8500.0) {
		tmp = a * 120.0;
	} else if (a <= -2.1e-258) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= 1.08e-101) {
		tmp = 60.0 * (x / (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 <= (-8500.0d0)) then
        tmp = a * 120.0d0
    else if (a <= (-2.1d-258)) then
        tmp = (-60.0d0) * ((x - y) / t)
    else if (a <= 1.08d-101) then
        tmp = 60.0d0 * (x / (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 <= -8500.0) {
		tmp = a * 120.0;
	} else if (a <= -2.1e-258) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= 1.08e-101) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8500.0:
		tmp = a * 120.0
	elif a <= -2.1e-258:
		tmp = -60.0 * ((x - y) / t)
	elif a <= 1.08e-101:
		tmp = 60.0 * (x / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8500.0)
		tmp = Float64(a * 120.0);
	elseif (a <= -2.1e-258)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	elseif (a <= 1.08e-101)
		tmp = Float64(60.0 * Float64(x / 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 <= -8500.0)
		tmp = a * 120.0;
	elseif (a <= -2.1e-258)
		tmp = -60.0 * ((x - y) / t);
	elseif (a <= 1.08e-101)
		tmp = 60.0 * (x / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8500.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -2.1e-258], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.08e-101], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8500 or 1.08e-101 < 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* 99.8%

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

      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 75.4%

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

   if -8500 < a < -2.0999999999999999e-258

   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 76.4%

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

   6. Taylor expanded in z around 0 55.2%

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

   if -2.0999999999999999e-258 < a < 1.08e-101

   1. Initial program 97.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf 58.1%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8500:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-258}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-101}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \frac{-60}{z - t} + a \cdot 120\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+34}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -9.5e+42)
   (+ (* y (/ -60.0 (- z t))) (* a 120.0))
   (if (<= y 9.5e+34)
     (+ (/ (* 60.0 x) (- z t)) (* a 120.0))
     (+ (/ (* y -60.0) (- z t)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -9.5e+42) {
		tmp = (y * (-60.0 / (z - t))) + (a * 120.0);
	} else if (y <= 9.5e+34) {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	} else {
		tmp = ((y * -60.0) / (z - t)) + (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 (y <= (-9.5d+42)) then
        tmp = (y * ((-60.0d0) / (z - t))) + (a * 120.0d0)
    else if (y <= 9.5d+34) then
        tmp = ((60.0d0 * x) / (z - t)) + (a * 120.0d0)
    else
        tmp = ((y * (-60.0d0)) / (z - t)) + (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 (y <= -9.5e+42) {
		tmp = (y * (-60.0 / (z - t))) + (a * 120.0);
	} else if (y <= 9.5e+34) {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	} else {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -9.5e+42:
		tmp = (y * (-60.0 / (z - t))) + (a * 120.0)
	elif y <= 9.5e+34:
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0)
	else:
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -9.5e+42)
		tmp = Float64(Float64(y * Float64(-60.0 / Float64(z - t))) + Float64(a * 120.0));
	elseif (y <= 9.5e+34)
		tmp = Float64(Float64(Float64(60.0 * x) / Float64(z - t)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -9.5e+42)
		tmp = (y * (-60.0 / (z - t))) + (a * 120.0);
	elseif (y <= 9.5e+34)
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	else
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -9.5e+42], N[(N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+34], N[(N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.50000000000000019e42

   1. Initial program 98.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 89.2%

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

      1. associate-*r/ 87.4%

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

      2. *-commutative 87.4%

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

      3. *-lft-identity 87.4%

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

      4. times-frac 89.1%

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

      5. /-rgt-identity 89.1%

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

   7. Simplified 89.1%

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

   if -9.50000000000000019e42 < y < 9.4999999999999999e34

   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 94.6%

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

      1. associate-*r/ 94.7%

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

   7. Simplified 94.7%

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

   if 9.4999999999999999e34 < y

   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 90.7%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \frac{-60}{z - t} + a \cdot 120\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+34}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{-50}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-258}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-179}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.6e-50)
   (* a 120.0)
   (if (<= a -1.3e-258)
     (/ (* 60.0 y) t)
     (if (<= a 2.9e-179) (* x (/ 60.0 z)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.6e-50) {
		tmp = a * 120.0;
	} else if (a <= -1.3e-258) {
		tmp = (60.0 * y) / t;
	} else if (a <= 2.9e-179) {
		tmp = x * (60.0 / 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 <= (-2.6d-50)) then
        tmp = a * 120.0d0
    else if (a <= (-1.3d-258)) then
        tmp = (60.0d0 * y) / t
    else if (a <= 2.9d-179) then
        tmp = x * (60.0d0 / 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 <= -2.6e-50) {
		tmp = a * 120.0;
	} else if (a <= -1.3e-258) {
		tmp = (60.0 * y) / t;
	} else if (a <= 2.9e-179) {
		tmp = x * (60.0 / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.6e-50:
		tmp = a * 120.0
	elif a <= -1.3e-258:
		tmp = (60.0 * y) / t
	elif a <= 2.9e-179:
		tmp = x * (60.0 / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.6e-50)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.3e-258)
		tmp = Float64(Float64(60.0 * y) / t);
	elseif (a <= 2.9e-179)
		tmp = Float64(x * Float64(60.0 / 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 <= -2.6e-50)
		tmp = a * 120.0;
	elseif (a <= -1.3e-258)
		tmp = (60.0 * y) / t;
	elseif (a <= 2.9e-179)
		tmp = x * (60.0 / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.6e-50], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.3e-258], N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 2.9e-179], N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.6000000000000001e-50 or 2.8999999999999999e-179 < a

   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 69.9%

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

   if -2.6000000000000001e-50 < a < -1.30000000000000009e-258

   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 x around 0 73.7%

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

      1. associate-*r/ 73.9%

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

      2. *-commutative 73.9%

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

      3. *-lft-identity 73.9%

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

      4. times-frac 73.7%

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

      5. /-rgt-identity 73.7%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in y around inf 73.6%

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

   9. Taylor expanded in z around 0 54.4%

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

   10. Taylor expanded in y around inf 40.9%

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

       1. associate-*r/ 41.0%

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

       2. *-commutative 41.0%

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

   12. Simplified 41.0%

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

   if -1.30000000000000009e-258 < a < 2.8999999999999999e-179

   1. Initial program 97.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf 62.2%

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

      1. associate-*r/ 62.3%

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

      2. associate-*l/ 62.3%

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

      3. *-commutative 62.3%

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

   9. Simplified 62.3%

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

   10. Taylor expanded in z around inf 37.8%

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

       1. associate-*r/ 37.9%

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

       2. *-commutative 37.9%

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

       3. associate-*r/ 37.9%

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

   12. Simplified 37.9%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{-50}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-258}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-179}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.4 \cdot 10^{-50}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-258}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-180}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.4e-50)
   (* a 120.0)
   (if (<= a -9e-258)
     (* 60.0 (/ y t))
     (if (<= a 2.35e-180) (* x (/ 60.0 z)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.4e-50) {
		tmp = a * 120.0;
	} else if (a <= -9e-258) {
		tmp = 60.0 * (y / t);
	} else if (a <= 2.35e-180) {
		tmp = x * (60.0 / 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 <= (-8.4d-50)) then
        tmp = a * 120.0d0
    else if (a <= (-9d-258)) then
        tmp = 60.0d0 * (y / t)
    else if (a <= 2.35d-180) then
        tmp = x * (60.0d0 / 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 <= -8.4e-50) {
		tmp = a * 120.0;
	} else if (a <= -9e-258) {
		tmp = 60.0 * (y / t);
	} else if (a <= 2.35e-180) {
		tmp = x * (60.0 / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.4e-50:
		tmp = a * 120.0
	elif a <= -9e-258:
		tmp = 60.0 * (y / t)
	elif a <= 2.35e-180:
		tmp = x * (60.0 / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.4e-50)
		tmp = Float64(a * 120.0);
	elseif (a <= -9e-258)
		tmp = Float64(60.0 * Float64(y / t));
	elseif (a <= 2.35e-180)
		tmp = Float64(x * Float64(60.0 / 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 <= -8.4e-50)
		tmp = a * 120.0;
	elseif (a <= -9e-258)
		tmp = 60.0 * (y / t);
	elseif (a <= 2.35e-180)
		tmp = x * (60.0 / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.4e-50], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -9e-258], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.35e-180], N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.4000000000000003e-50 or 2.34999999999999988e-180 < a

   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 69.9%

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

   if -8.4000000000000003e-50 < a < -9.00000000000000017e-258

   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 x around 0 73.7%

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

      1. associate-*r/ 73.9%

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

      2. *-commutative 73.9%

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

      3. *-lft-identity 73.9%

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

      4. times-frac 73.7%

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

      5. /-rgt-identity 73.7%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in y around inf 73.6%

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

   9. Taylor expanded in z around 0 54.4%

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

   10. Taylor expanded in y around inf 40.9%

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

   if -9.00000000000000017e-258 < a < 2.34999999999999988e-180

   1. Initial program 97.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf 62.2%

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

      1. associate-*r/ 62.3%

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

      2. associate-*l/ 62.3%

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

      3. *-commutative 62.3%

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

   9. Simplified 62.3%

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

   10. Taylor expanded in z around inf 37.8%

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

       1. associate-*r/ 37.9%

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

       2. *-commutative 37.9%

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

       3. associate-*r/ 37.9%

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

   12. Simplified 37.9%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.4 \cdot 10^{-50}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-258}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-180}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{-48}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-257}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-179}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.6e-48)
   (* a 120.0)
   (if (<= a -3e-257)
     (* 60.0 (/ y t))
     (if (<= a 4.8e-179) (* 60.0 (/ x z)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.6e-48) {
		tmp = a * 120.0;
	} else if (a <= -3e-257) {
		tmp = 60.0 * (y / t);
	} else if (a <= 4.8e-179) {
		tmp = 60.0 * (x / 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 <= (-8.6d-48)) then
        tmp = a * 120.0d0
    else if (a <= (-3d-257)) then
        tmp = 60.0d0 * (y / t)
    else if (a <= 4.8d-179) then
        tmp = 60.0d0 * (x / 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 <= -8.6e-48) {
		tmp = a * 120.0;
	} else if (a <= -3e-257) {
		tmp = 60.0 * (y / t);
	} else if (a <= 4.8e-179) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.6e-48:
		tmp = a * 120.0
	elif a <= -3e-257:
		tmp = 60.0 * (y / t)
	elif a <= 4.8e-179:
		tmp = 60.0 * (x / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.6e-48)
		tmp = Float64(a * 120.0);
	elseif (a <= -3e-257)
		tmp = Float64(60.0 * Float64(y / t));
	elseif (a <= 4.8e-179)
		tmp = Float64(60.0 * Float64(x / 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 <= -8.6e-48)
		tmp = a * 120.0;
	elseif (a <= -3e-257)
		tmp = 60.0 * (y / t);
	elseif (a <= 4.8e-179)
		tmp = 60.0 * (x / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.6e-48], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -3e-257], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e-179], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.6e-48 or 4.8000000000000001e-179 < a

   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 69.9%

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

   if -8.6e-48 < a < -2.9999999999999999e-257

   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 x around 0 73.7%

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

      1. associate-*r/ 73.9%

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

      2. *-commutative 73.9%

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

      3. *-lft-identity 73.9%

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

      4. times-frac 73.7%

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

      5. /-rgt-identity 73.7%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in y around inf 73.6%

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

   9. Taylor expanded in z around 0 54.4%

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

   10. Taylor expanded in y around inf 40.9%

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

   if -2.9999999999999999e-257 < a < 4.8000000000000001e-179

   1. Initial program 97.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf 62.2%

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

   8. Taylor expanded in z around inf 37.8%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{-48}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-257}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-179}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7200 \lor \neg \left(a \leq 1.8 \cdot 10^{-83}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7200.0) (not (<= a 1.8e-83)))
   (* a 120.0)
   (* -60.0 (/ (- x y) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7200.0) || !(a <= 1.8e-83)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / 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 <= (-7200.0d0)) .or. (.not. (a <= 1.8d-83))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * ((x - y) / 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 <= -7200.0) || !(a <= 1.8e-83)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7200.0) or not (a <= 1.8e-83):
		tmp = a * 120.0
	else:
		tmp = -60.0 * ((x - y) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7200.0) || !(a <= 1.8e-83))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -7200.0) || ~((a <= 1.8e-83)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * ((x - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7200.0], N[Not[LessEqual[a, 1.8e-83]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7200 or 1.80000000000000006e-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* 99.8%

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

      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 76.3%

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

   if -7200 < a < 1.80000000000000006e-83

   1. Initial program 98.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 a around 0 83.9%

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

   6. Taylor expanded in z around 0 49.1%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7200 \lor \neg \left(a \leq 1.8 \cdot 10^{-83}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 53.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-226} \lor \neg \left(a \leq 7.6 \cdot 10^{-179}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.5e-226) (not (<= a 7.6e-179))) (* a 120.0) (* 60.0 (/ x z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.5e-226) || !(a <= 7.6e-179)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (x / 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 ((a <= (-5.5d-226)) .or. (.not. (a <= 7.6d-179))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * (x / 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 ((a <= -5.5e-226) || !(a <= 7.6e-179)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.5e-226) or not (a <= 7.6e-179):
		tmp = a * 120.0
	else:
		tmp = 60.0 * (x / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.5e-226) || !(a <= 7.6e-179))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.5e-226) || ~((a <= 7.6e-179)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.5e-226], N[Not[LessEqual[a, 7.6e-179]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.5e-226 or 7.59999999999999947e-179 < a

   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 61.6%

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

   if -5.5e-226 < a < 7.59999999999999947e-179

   1. Initial program 97.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 99.5%

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

      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 54.3%

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

   8. Taylor expanded in z around inf 34.3%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-226} \lor \neg \left(a \leq 7.6 \cdot 10^{-179}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 52.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.4 \cdot 10^{-225} \lor \neg \left(a \leq 2.45 \cdot 10^{-195}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8.4e-225) (not (<= a 2.45e-195)))
   (* a 120.0)
   (* -60.0 (/ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.4e-225) || !(a <= 2.45e-195)) {
		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 ((a <= (-8.4d-225)) .or. (.not. (a <= 2.45d-195))) 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 ((a <= -8.4e-225) || !(a <= 2.45e-195)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8.4e-225) or not (a <= 2.45e-195):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (x / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8.4e-225) || !(a <= 2.45e-195))
		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 ((a <= -8.4e-225) || ~((a <= 2.45e-195)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8.4e-225], N[Not[LessEqual[a, 2.45e-195]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.40000000000000001e-225 or 2.4500000000000002e-195 < a

   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 60.8%

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

   if -8.40000000000000001e-225 < a < 2.4500000000000002e-195

   1. Initial program 97.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 99.5%

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

      3. clear-num 99.4%

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

      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 55.6%

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

   8. Taylor expanded in z around 0 28.9%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.4 \cdot 10^{-225} \lor \neg \left(a \leq 2.45 \cdot 10^{-195}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 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]

Derivation

1. Initial program 99.4%

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

Alternative 18: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return ((x - y) * (60.0 / (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 = ((x - y) * (60.0d0 / (z - t))) + (a * 120.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. *-commutative 99.4%

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

   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. Add Preprocessing

Alternative 19: 99.8% accurate, 1.0× speedup

Math

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

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(60.0 * Float64(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[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

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

Alternative 20: 51.3% 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 99.4%

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

   1. *-commutative 99.4%

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

   2. associate-/l* 99.8%

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

   3. fma-define 99.7%

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

   4. sub-neg 99.7%

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

   5. +-commutative 99.7%

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

   6. neg-sub0 99.7%

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

   7. associate-+l- 99.7%

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

   8. sub0-neg 99.7%

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

   9. distribute-frac-neg2 99.7%

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

   10. distribute-neg-frac 99.7%

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

   11. metadata-eval 99.7%

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

3. Simplified 99.7%

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

5. Taylor expanded in t around inf 51.6%

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

6. Final simplification 51.6%

   \[\leadsto a \cdot 120 \]
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 2024150 
(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)))