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

Percentage Accurate: 99.4% → 99.4%

Time: 11.9s

Alternatives: 16

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. +-commutative N/A

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

   2. accelerator-lowering-fma.f64 N/A

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

   3. /-lowering-/.f64 N/A

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

   4. *-lowering-*.f64 N/A

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

   5. --lowering--.f64 N/A

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

   6. --lowering--.f64 99.8

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

4. Applied egg-rr 99.8%

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

Alternative 2: 60.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot -60}{t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+178}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) -60.0) t)) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -5e+94) t_1 (if (<= t_2 1e+178) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * -60.0) / t;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+94) {
		tmp = t_1;
	} else if (t_2 <= 1e+178) {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = ((x - y) * (-60.0d0)) / t
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-5d+94)) then
        tmp = t_1
    else if (t_2 <= 1d+178) then
        tmp = 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 = ((x - y) * -60.0) / t;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+94) {
		tmp = t_1;
	} else if (t_2 <= 1e+178) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * -60.0) / t
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -5e+94:
		tmp = t_1
	elif t_2 <= 1e+178:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * -60.0) / t)
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+94)
		tmp = t_1;
	elseif (t_2 <= 1e+178)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) * -60.0) / t;
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+94)
		tmp = t_1;
	elseif (t_2 <= 1e+178)
		tmp = 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[(N[(x - y), $MachinePrecision] * -60.0), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+94], t$95$1, If[LessEqual[t$95$2, 1e+178], N[(a * 120.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.0000000000000001e94 or 1.0000000000000001e178 < (/.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. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. *-lowering-*.f64 64.0

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

   5. Simplified 64.0%

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

   6. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 55.7

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

   8. Simplified 55.7%

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

   if -5.0000000000000001e94 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.0000000000000001e178

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 69.1

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

   5. Simplified 69.1%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+94}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot -60}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+178}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot -60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 55.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+227}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{+178}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+227)
     (/ (* 60.0 y) t)
     (if (<= t_1 1e+178) (* a 120.0) (* y (/ 60.0 t))))))

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 <= -1e+227) {
		tmp = (60.0 * y) / t;
	} else if (t_1 <= 1e+178) {
		tmp = a * 120.0;
	} else {
		tmp = y * (60.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-1d+227)) then
        tmp = (60.0d0 * y) / t
    else if (t_1 <= 1d+178) then
        tmp = a * 120.0d0
    else
        tmp = y * (60.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+227) {
		tmp = (60.0 * y) / t;
	} else if (t_1 <= 1e+178) {
		tmp = a * 120.0;
	} else {
		tmp = y * (60.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+227:
		tmp = (60.0 * y) / t
	elif t_1 <= 1e+178:
		tmp = a * 120.0
	else:
		tmp = y * (60.0 / t)
	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 <= -1e+227)
		tmp = Float64(Float64(60.0 * y) / t);
	elseif (t_1 <= 1e+178)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(y * Float64(60.0 / t));
	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 <= -1e+227)
		tmp = (60.0 * y) / t;
	elseif (t_1 <= 1e+178)
		tmp = a * 120.0;
	else
		tmp = y * (60.0 / t);
	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, -1e+227], N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 1e+178], N[(a * 120.0), $MachinePrecision], N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.0000000000000001e227

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. *-lowering-*.f64 62.0

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

   5. Simplified 62.0%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. /-lowering-/.f64 N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 52.2

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

   8. Simplified 52.2%

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

   if -1.0000000000000001e227 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.0000000000000001e178

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 65.0

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

   5. Simplified 65.0%

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

   if 1.0000000000000001e178 < (/.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. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. *-lowering-*.f64 59.9

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

   5. Simplified 59.9%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. /-lowering-/.f64 N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 39.1

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

   8. Simplified 39.1%

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

      1. associate-*r/ N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. associate-*r* N/A

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

      5. div-inv N/A

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

      6. *-lowering-*.f64 N/A

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

      7. /-lowering-/.f64 39.1

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

   10. Applied egg-rr 39.1%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+227}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+178}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 55.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{60}{t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+178}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ 60.0 t))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -1e+227) t_1 (if (<= t_2 1e+178) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (60.0 / t);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+227) {
		tmp = t_1;
	} else if (t_2 <= 1e+178) {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = y * (60.0d0 / t)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-1d+227)) then
        tmp = t_1
    else if (t_2 <= 1d+178) then
        tmp = 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 = y * (60.0 / t);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+227) {
		tmp = t_1;
	} else if (t_2 <= 1e+178) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (60.0 / t)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -1e+227:
		tmp = t_1
	elif t_2 <= 1e+178:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(60.0 / t))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+227)
		tmp = t_1;
	elseif (t_2 <= 1e+178)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (60.0 / t);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+227)
		tmp = t_1;
	elseif (t_2 <= 1e+178)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+227], t$95$1, If[LessEqual[t$95$2, 1e+178], N[(a * 120.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.0000000000000001e227 or 1.0000000000000001e178 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. *-lowering-*.f64 60.8

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

   5. Simplified 60.8%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. /-lowering-/.f64 N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 44.3

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

   8. Simplified 44.3%

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

      1. associate-*r/ N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. associate-*r* N/A

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

      5. div-inv N/A

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

      6. *-lowering-*.f64 N/A

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

      7. /-lowering-/.f64 44.3

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

   10. Applied egg-rr 44.3%

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

   if -1.0000000000000001e227 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.0000000000000001e178

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 65.0

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

   5. Simplified 65.0%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+227}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+178}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{60}{z}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+239}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+181}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ 60.0 z))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -5e+239) t_1 (if (<= t_2 1e+181) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (60.0 / z);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+239) {
		tmp = t_1;
	} else if (t_2 <= 1e+181) {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = x * (60.0d0 / z)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-5d+239)) then
        tmp = t_1
    else if (t_2 <= 1d+181) then
        tmp = 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 = x * (60.0 / z);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+239) {
		tmp = t_1;
	} else if (t_2 <= 1e+181) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (60.0 / z)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -5e+239:
		tmp = t_1
	elif t_2 <= 1e+181:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(60.0 / z))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+239)
		tmp = t_1;
	elseif (t_2 <= 1e+181)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (60.0 / z);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+239)
		tmp = t_1;
	elseif (t_2 <= 1e+181)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+239], t$95$1, If[LessEqual[t$95$2, 1e+181], N[(a * 120.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.00000000000000007e239 or 9.9999999999999992e180 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. /-lowering-/.f64 N/A

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

      9. --lowering--.f64 43.0

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

   5. Simplified 43.0%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 31.3%

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

   if -5.00000000000000007e239 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999992e180

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 64.3

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

   5. Simplified 64.3%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+239}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+181}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{-60}{t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+178}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ -60.0 t))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -5e+245) t_1 (if (<= t_2 1e+178) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (-60.0 / t);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+245) {
		tmp = t_1;
	} else if (t_2 <= 1e+178) {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = x * ((-60.0d0) / t)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-5d+245)) then
        tmp = t_1
    else if (t_2 <= 1d+178) then
        tmp = 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 = x * (-60.0 / t);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+245) {
		tmp = t_1;
	} else if (t_2 <= 1e+178) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (-60.0 / t)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -5e+245:
		tmp = t_1
	elif t_2 <= 1e+178:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(-60.0 / t))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+245)
		tmp = t_1;
	elseif (t_2 <= 1e+178)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (-60.0 / t);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+245)
		tmp = t_1;
	elseif (t_2 <= 1e+178)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+245], t$95$1, If[LessEqual[t$95$2, 1e+178], N[(a * 120.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.00000000000000034e245 or 1.0000000000000001e178 < (/.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. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. /-lowering-/.f64 N/A

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

      9. --lowering--.f64 45.4

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

   5. Simplified 45.4%

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

   6. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 30.5

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

   8. Simplified 30.5%

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

   if -5.00000000000000034e245 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.0000000000000001e178

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 64.2

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

   5. Simplified 64.2%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+245}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+178}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-63}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-210}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-88}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -5e-63)
   (* a 120.0)
   (if (<= (* a 120.0) 1e-210)
     (* y (/ 60.0 (- t z)))
     (if (<= (* a 120.0) 1e-88)
       (/ x (* (- z t) 0.016666666666666666))
       (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e-63) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-210) {
		tmp = y * (60.0 / (t - z));
	} else if ((a * 120.0) <= 1e-88) {
		tmp = x / ((z - t) * 0.016666666666666666);
	} 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 * 120.0d0) <= (-5d-63)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-210) then
        tmp = y * (60.0d0 / (t - z))
    else if ((a * 120.0d0) <= 1d-88) then
        tmp = x / ((z - t) * 0.016666666666666666d0)
    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 * 120.0) <= -5e-63) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-210) {
		tmp = y * (60.0 / (t - z));
	} else if ((a * 120.0) <= 1e-88) {
		tmp = x / ((z - t) * 0.016666666666666666);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -5e-63:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-210:
		tmp = y * (60.0 / (t - z))
	elif (a * 120.0) <= 1e-88:
		tmp = x / ((z - t) * 0.016666666666666666)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e-63)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-210)
		tmp = Float64(y * Float64(60.0 / Float64(t - z)));
	elseif (Float64(a * 120.0) <= 1e-88)
		tmp = Float64(x / Float64(Float64(z - t) * 0.016666666666666666));
	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 * 120.0) <= -5e-63)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-210)
		tmp = y * (60.0 / (t - z));
	elseif ((a * 120.0) <= 1e-88)
		tmp = x / ((z - t) * 0.016666666666666666);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-63], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-210], N[(y * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-88], N[(x / N[(N[(z - t), $MachinePrecision] * 0.016666666666666666), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.0000000000000002e-63 or 9.99999999999999934e-89 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 73.0

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

   5. Simplified 73.0%

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

   if -5.0000000000000002e-63 < (*.f64 a #s(literal 120 binary64)) < 1e-210

   1. Initial program 99.6%

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. --lowering--.f64 99.6

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 56.2

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

   7. Simplified 56.2%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. frac-2neg N/A

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

      5. metadata-eval N/A

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

      6. /-lowering-/.f64 N/A

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

      7. neg-sub0 N/A

         \[\leadsto \frac{60}{\color{blue}{0 - \left(z - t\right)}} \cdot y \]

      8. sub-neg N/A

         \[\leadsto \frac{60}{0 - \color{blue}{\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)}} \cdot y \]

      9. +-commutative N/A

         \[\leadsto \frac{60}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)}} \cdot y \]

      10. associate--r+ N/A

          \[\leadsto \frac{60}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(t\right)\right)\right) - z}} \cdot y \]

      11. neg-sub0 N/A

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

      12. remove-double-neg N/A

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

      13. --lowering--.f64 56.2

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

   9. Applied egg-rr 56.2%

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

   if 1e-210 < (*.f64 a #s(literal 120 binary64)) < 9.99999999999999934e-89

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. /-lowering-/.f64 N/A

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

      9. --lowering--.f64 51.1

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

   5. Simplified 51.1%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

      3. /-lowering-/.f64 N/A

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

      4. div-inv N/A

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

      5. *-lowering-*.f64 N/A

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

      6. --lowering--.f64 N/A

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

      7. metadata-eval 51.3

         \[\leadsto \frac{x}{\left(z - t\right) \cdot \color{blue}{0.016666666666666666}} \]

   7. Applied egg-rr 51.3%

      \[\leadsto \color{blue}{\frac{x}{\left(z - t\right) \cdot 0.016666666666666666}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-63}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-210}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-88}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-63}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-210}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-88}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -5e-63)
   (* a 120.0)
   (if (<= (* a 120.0) 1e-210)
     (* y (/ 60.0 (- t z)))
     (if (<= (* a 120.0) 1e-88) (* x (/ 60.0 (- z t))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e-63) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-210) {
		tmp = y * (60.0 / (t - z));
	} else if ((a * 120.0) <= 1e-88) {
		tmp = x * (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 * 120.0d0) <= (-5d-63)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-210) then
        tmp = y * (60.0d0 / (t - z))
    else if ((a * 120.0d0) <= 1d-88) then
        tmp = x * (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 * 120.0) <= -5e-63) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-210) {
		tmp = y * (60.0 / (t - z));
	} else if ((a * 120.0) <= 1e-88) {
		tmp = x * (60.0 / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -5e-63:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-210:
		tmp = y * (60.0 / (t - z))
	elif (a * 120.0) <= 1e-88:
		tmp = x * (60.0 / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e-63)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-210)
		tmp = Float64(y * Float64(60.0 / Float64(t - z)));
	elseif (Float64(a * 120.0) <= 1e-88)
		tmp = Float64(x * 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 * 120.0) <= -5e-63)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-210)
		tmp = y * (60.0 / (t - z));
	elseif ((a * 120.0) <= 1e-88)
		tmp = x * (60.0 / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-63], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-210], N[(y * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-88], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.0000000000000002e-63 or 9.99999999999999934e-89 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 73.0

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

   5. Simplified 73.0%

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

   if -5.0000000000000002e-63 < (*.f64 a #s(literal 120 binary64)) < 1e-210

   1. Initial program 99.6%

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. --lowering--.f64 99.6

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 56.2

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

   7. Simplified 56.2%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. frac-2neg N/A

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

      5. metadata-eval N/A

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

      6. /-lowering-/.f64 N/A

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

      7. neg-sub0 N/A

         \[\leadsto \frac{60}{\color{blue}{0 - \left(z - t\right)}} \cdot y \]

      8. sub-neg N/A

         \[\leadsto \frac{60}{0 - \color{blue}{\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)}} \cdot y \]

      9. +-commutative N/A

         \[\leadsto \frac{60}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)}} \cdot y \]

      10. associate--r+ N/A

          \[\leadsto \frac{60}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(t\right)\right)\right) - z}} \cdot y \]

      11. neg-sub0 N/A

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

      12. remove-double-neg N/A

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

      13. --lowering--.f64 56.2

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

   9. Applied egg-rr 56.2%

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

   if 1e-210 < (*.f64 a #s(literal 120 binary64)) < 9.99999999999999934e-89

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. /-lowering-/.f64 N/A

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

      9. --lowering--.f64 51.1

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

   5. Simplified 51.1%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-63}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-210}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-88}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-63}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-210}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-88}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -5e-63)
   (* a 120.0)
   (if (<= (* a 120.0) 1e-210)
     (* -60.0 (/ y (- z t)))
     (if (<= (* a 120.0) 1e-88) (* x (/ 60.0 (- z t))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e-63) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-210) {
		tmp = -60.0 * (y / (z - t));
	} else if ((a * 120.0) <= 1e-88) {
		tmp = x * (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 * 120.0d0) <= (-5d-63)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-210) then
        tmp = (-60.0d0) * (y / (z - t))
    else if ((a * 120.0d0) <= 1d-88) then
        tmp = x * (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 * 120.0) <= -5e-63) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-210) {
		tmp = -60.0 * (y / (z - t));
	} else if ((a * 120.0) <= 1e-88) {
		tmp = x * (60.0 / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -5e-63:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-210:
		tmp = -60.0 * (y / (z - t))
	elif (a * 120.0) <= 1e-88:
		tmp = x * (60.0 / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e-63)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-210)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 1e-88)
		tmp = Float64(x * 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 * 120.0) <= -5e-63)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-210)
		tmp = -60.0 * (y / (z - t));
	elseif ((a * 120.0) <= 1e-88)
		tmp = x * (60.0 / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-63], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-210], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-88], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.0000000000000002e-63 or 9.99999999999999934e-89 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 73.0

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

   5. Simplified 73.0%

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

   if -5.0000000000000002e-63 < (*.f64 a #s(literal 120 binary64)) < 1e-210

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. --lowering--.f64 56.2

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

   5. Simplified 56.2%

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

   if 1e-210 < (*.f64 a #s(literal 120 binary64)) < 9.99999999999999934e-89

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. /-lowering-/.f64 N/A

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

      9. --lowering--.f64 51.1

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

   5. Simplified 51.1%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-63}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-210}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-88}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{+23}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -4e-14)
   (* a 120.0)
   (if (<= (* a 120.0) 4e+23) (/ (* 60.0 (- x y)) (- z t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e-14) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 4e+23) {
		tmp = (60.0 * (x - y)) / (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 * 120.0d0) <= (-4d-14)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 4d+23) then
        tmp = (60.0d0 * (x - y)) / (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 * 120.0) <= -4e-14) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 4e+23) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -4e-14:
		tmp = a * 120.0
	elif (a * 120.0) <= 4e+23:
		tmp = (60.0 * (x - y)) / (z - t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e-14)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 4e+23)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / 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 * 120.0) <= -4e-14)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 4e+23)
		tmp = (60.0 * (x - y)) / (z - t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-14], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 4e+23], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -4e-14 or 3.9999999999999997e23 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 85.1

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

   5. Simplified 85.1%

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

   if -4e-14 < (*.f64 a #s(literal 120 binary64)) < 3.9999999999999997e23

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. --lowering--.f64 77.1

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

   5. Simplified 77.1%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{+23}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{-222}:\\ \;\;\;\;\mathsf{fma}\left(120, a, x \cdot \frac{60}{z - t}\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{z \cdot 0.016666666666666666}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma -60.0 (/ (- x y) t) (* a 120.0))))
   (if (<= t -3.2e+17)
     t_1
     (if (<= t -1.16e-222)
       (fma 120.0 a (* x (/ 60.0 (- z t))))
       (if (<= t 7.5e-7)
         (fma a 120.0 (/ (- x y) (* z 0.016666666666666666)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-60.0, ((x - y) / t), (a * 120.0));
	double tmp;
	if (t <= -3.2e+17) {
		tmp = t_1;
	} else if (t <= -1.16e-222) {
		tmp = fma(120.0, a, (x * (60.0 / (z - t))));
	} else if (t <= 7.5e-7) {
		tmp = fma(a, 120.0, ((x - y) / (z * 0.016666666666666666)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(-60.0, Float64(Float64(x - y) / t), Float64(a * 120.0))
	tmp = 0.0
	if (t <= -3.2e+17)
		tmp = t_1;
	elseif (t <= -1.16e-222)
		tmp = fma(120.0, a, Float64(x * Float64(60.0 / Float64(z - t))));
	elseif (t <= 7.5e-7)
		tmp = fma(a, 120.0, Float64(Float64(x - y) / Float64(z * 0.016666666666666666)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.2e+17], t$95$1, If[LessEqual[t, -1.16e-222], N[(120.0 * a + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e-7], N[(a * 120.0 + N[(N[(x - y), $MachinePrecision] / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.2e17 or 7.5000000000000002e-7 < t

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. *-lowering-*.f64 92.9

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

   5. Simplified 92.9%

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

   if -3.2e17 < t < -1.16e-222

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 82.3

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

   5. Simplified 82.3%

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

   if -1.16e-222 < t < 7.5000000000000002e-7

   1. Initial program 99.9%

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. --lowering--.f64 99.9

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

   4. Applied egg-rr 99.9%

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. /-lowering-/.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. div-inv N/A

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

      9. *-lowering-*.f64 N/A

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

      10. --lowering--.f64 N/A

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

      11. metadata-eval 99.8

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{x - y}{\left(z - t\right) \cdot \color{blue}{0.016666666666666666}}\right) \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}\right)} \]

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{x - y}{\color{blue}{z} \cdot \frac{1}{60}}\right) \]
   8. Step-by-step derivation

   9. Simplified 86.5%

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{x - y}{\color{blue}{z} \cdot 0.016666666666666666}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{-222}:\\ \;\;\;\;\mathsf{fma}\left(120, a, x \cdot \frac{60}{z - t}\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{z \cdot 0.016666666666666666}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 83.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-222}:\\ \;\;\;\;\mathsf{fma}\left(120, a, x \cdot \frac{60}{z - t}\right)\\ \mathbf{elif}\;t \leq 3.35 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma -60.0 (/ (- x y) t) (* a 120.0))))
   (if (<= t -1e+19)
     t_1
     (if (<= t -1.5e-222)
       (fma 120.0 a (* x (/ 60.0 (- z t))))
       (if (<= t 3.35e-6) (fma 60.0 (/ (- x y) z) (* a 120.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-60.0, ((x - y) / t), (a * 120.0));
	double tmp;
	if (t <= -1e+19) {
		tmp = t_1;
	} else if (t <= -1.5e-222) {
		tmp = fma(120.0, a, (x * (60.0 / (z - t))));
	} else if (t <= 3.35e-6) {
		tmp = fma(60.0, ((x - y) / z), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(-60.0, Float64(Float64(x - y) / t), Float64(a * 120.0))
	tmp = 0.0
	if (t <= -1e+19)
		tmp = t_1;
	elseif (t <= -1.5e-222)
		tmp = fma(120.0, a, Float64(x * Float64(60.0 / Float64(z - t))));
	elseif (t <= 3.35e-6)
		tmp = fma(60.0, Float64(Float64(x - y) / z), Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e+19], t$95$1, If[LessEqual[t, -1.5e-222], N[(120.0 * a + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.35e-6], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1e19 or 3.35e-6 < t

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. *-lowering-*.f64 92.9

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

   5. Simplified 92.9%

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

   if -1e19 < t < -1.50000000000000015e-222

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 82.3

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

   5. Simplified 82.3%

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

   if -1.50000000000000015e-222 < t < 3.35e-6

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. *-lowering-*.f64 86.5

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

   5. Simplified 86.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-222}:\\ \;\;\;\;\mathsf{fma}\left(120, a, x \cdot \frac{60}{z - t}\right)\\ \mathbf{elif}\;t \leq 3.35 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-63}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{+23}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -5e-63)
   (* a 120.0)
   (if (<= (* a 120.0) 4e+23) (* -60.0 (/ y (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e-63) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 4e+23) {
		tmp = -60.0 * (y / (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 * 120.0d0) <= (-5d-63)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 4d+23) then
        tmp = (-60.0d0) * (y / (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 * 120.0) <= -5e-63) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 4e+23) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -5e-63:
		tmp = a * 120.0
	elif (a * 120.0) <= 4e+23:
		tmp = -60.0 * (y / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e-63)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 4e+23)
		tmp = Float64(-60.0 * Float64(y / 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 * 120.0) <= -5e-63)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 4e+23)
		tmp = -60.0 * (y / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-63], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 4e+23], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.0000000000000002e-63 or 3.9999999999999997e23 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 82.9

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

   5. Simplified 82.9%

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

   if -5.0000000000000002e-63 < (*.f64 a #s(literal 120 binary64)) < 3.9999999999999997e23

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. --lowering--.f64 45.3

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

   5. Simplified 45.3%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-63}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{+23}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 88.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(120, a, x \cdot \frac{60}{z - t}\right)\\ \mathbf{if}\;x \leq -9.6 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 26000000000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{-60}{z - t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma 120.0 a (* x (/ 60.0 (- z t))))))
   (if (<= x -9.6e+159)
     t_1
     (if (<= x 26000000000.0) (fma 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 = fma(120.0, a, (x * (60.0 / (z - t))));
	double tmp;
	if (x <= -9.6e+159) {
		tmp = t_1;
	} else if (x <= 26000000000.0) {
		tmp = fma(y, (-60.0 / (z - t)), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(120.0, a, Float64(x * Float64(60.0 / Float64(z - t))))
	tmp = 0.0
	if (x <= -9.6e+159)
		tmp = t_1;
	elseif (x <= 26000000000.0)
		tmp = fma(y, Float64(-60.0 / Float64(z - t)), Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(120.0 * a + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.6e+159], t$95$1, If[LessEqual[x, 26000000000.0], N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5999999999999999e159 or 2.6e10 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 87.8

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

   5. Simplified 87.8%

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

   if -9.5999999999999999e159 < x < 2.6e10

   1. Initial program 99.8%

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. --lowering--.f64 99.8

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

      13. /-lowering-/.f64 N/A

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

      14. --lowering--.f64 N/A

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

      15. *-lowering-*.f64 95.1

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

   7. Simplified 95.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{-60}{z - t}, 120 \cdot a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+159}:\\ \;\;\;\;\mathsf{fma}\left(120, a, x \cdot \frac{60}{z - t}\right)\\ \mathbf{elif}\;x \leq 26000000000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{-60}{z - t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(120, a, x \cdot \frac{60}{z - t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 83.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-87}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma 60.0 (/ (- x y) z) (* a 120.0))))
   (if (<= z -9.8e+14)
     t_1
     (if (<= z 5.7e-87) (fma -60.0 (/ (- x y) t) (* a 120.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(60.0, ((x - y) / z), (a * 120.0));
	double tmp;
	if (z <= -9.8e+14) {
		tmp = t_1;
	} else if (z <= 5.7e-87) {
		tmp = fma(-60.0, ((x - y) / t), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(60.0, Float64(Float64(x - y) / z), Float64(a * 120.0))
	tmp = 0.0
	if (z <= -9.8e+14)
		tmp = t_1;
	elseif (z <= 5.7e-87)
		tmp = fma(-60.0, Float64(Float64(x - y) / t), Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.8e+14], t$95$1, If[LessEqual[z, 5.7e-87], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.8e14 or 5.7e-87 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. *-lowering-*.f64 86.8

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

   5. Simplified 86.8%

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

   if -9.8e14 < z < 5.7e-87

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. *-lowering-*.f64 87.2

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

   5. Simplified 87.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-87}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.7% accurate, 5.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{120 \cdot a} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 54.7

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

5. Simplified 54.7%

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

6. Final simplification 54.7%

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

Developer Target 1: 99.7% accurate, 0.8× 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 2024198 
(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)))