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

Percentage Accurate: 99.4% → 99.8%

Time: 12.5s

Alternatives: 22

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: 99.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. clear-num N/A

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

   5. un-div-inv N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 99.8

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

4. Applied rewrites 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{0.016666666666666666 \cdot \left(z - t\right)}\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-27}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x y) (* 0.016666666666666666 (- z t))))
        (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -2e+39) t_1 (if (<= t_2 5e-27) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) / (0.016666666666666666 * (z - t));
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+39) {
		tmp = t_1;
	} else if (t_2 <= 5e-27) {
		tmp = 120.0 * a;
	} 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) / (0.016666666666666666d0 * (z - t))
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-2d+39)) then
        tmp = t_1
    else if (t_2 <= 5d-27) then
        tmp = 120.0d0 * a
    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) / (0.016666666666666666 * (z - t));
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+39) {
		tmp = t_1;
	} else if (t_2 <= 5e-27) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - y) / (0.016666666666666666 * (z - t))
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -2e+39:
		tmp = t_1
	elif t_2 <= 5e-27:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) / Float64(0.016666666666666666 * Float64(z - t)))
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+39)
		tmp = t_1;
	elseif (t_2 <= 5e-27)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - y) / (0.016666666666666666 * (z - t));
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e+39)
		tmp = t_1;
	elseif (t_2 <= 5e-27)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(0.016666666666666666 * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+39], t$95$1, If[LessEqual[t$95$2, 5e-27], N[(120.0 * a), $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)) < -1.99999999999999988e39 or 5.0000000000000002e-27 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 77.6

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

   5. Applied rewrites 77.6%

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

   7. Applied rewrites 77.7%

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

   if -1.99999999999999988e39 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.0000000000000002e-27

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 78.2

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

   5. Applied rewrites 78.2%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+39}:\\ \;\;\;\;\frac{x - y}{0.016666666666666666 \cdot \left(z - t\right)}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{-27}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{0.016666666666666666 \cdot \left(z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+123}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{0.016666666666666666 \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -1e+82)
     (* (/ x (- z t)) 60.0)
     (if (<= t_1 5e+123) (* 120.0 a) (/ (- x y) (* 0.016666666666666666 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -1e+82) {
		tmp = (x / (z - t)) * 60.0;
	} else if (t_1 <= 5e+123) {
		tmp = 120.0 * a;
	} else {
		tmp = (x - y) / (0.016666666666666666 * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x - y) * 60.0d0) / (z - t)
    if (t_1 <= (-1d+82)) then
        tmp = (x / (z - t)) * 60.0d0
    else if (t_1 <= 5d+123) then
        tmp = 120.0d0 * a
    else
        tmp = (x - y) / (0.016666666666666666d0 * z)
    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) / (z - t);
	double tmp;
	if (t_1 <= -1e+82) {
		tmp = (x / (z - t)) * 60.0;
	} else if (t_1 <= 5e+123) {
		tmp = 120.0 * a;
	} else {
		tmp = (x - y) / (0.016666666666666666 * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_1 <= -1e+82:
		tmp = (x / (z - t)) * 60.0
	elif t_1 <= 5e+123:
		tmp = 120.0 * a
	else:
		tmp = (x - y) / (0.016666666666666666 * z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+82)
		tmp = Float64(Float64(x / Float64(z - t)) * 60.0);
	elseif (t_1 <= 5e+123)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x - y) / Float64(0.016666666666666666 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+82)
		tmp = (x / (z - t)) * 60.0;
	elseif (t_1 <= 5e+123)
		tmp = 120.0 * a;
	else
		tmp = (x - y) / (0.016666666666666666 * z);
	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] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+82], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+123], N[(120.0 * a), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(0.016666666666666666 * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.9999999999999996e81

   1. Initial program 97.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 57.6

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

   5. Applied rewrites 57.6%

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

   if -9.9999999999999996e81 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999974e123

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 71.6

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

   5. Applied rewrites 71.6%

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

   if 4.99999999999999974e123 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.2%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 88.7

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

   5. Applied rewrites 88.7%

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

   7. Applied rewrites 89.0%

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

   8. Taylor expanded in t around 0

      \[\leadsto \frac{x - y}{\frac{1}{60} \cdot \color{blue}{z}} \]
   9. Step-by-step derivation

   10. Applied rewrites 63.9%

       \[\leadsto \frac{x - y}{0.016666666666666666 \cdot \color{blue}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+123}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{0.016666666666666666 \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+123}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -1e+82)
     (* (/ x (- z t)) 60.0)
     (if (<= t_1 5e+123) (* 120.0 a) (* (/ (- x y) z) 60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -1e+82) {
		tmp = (x / (z - t)) * 60.0;
	} else if (t_1 <= 5e+123) {
		tmp = 120.0 * a;
	} else {
		tmp = ((x - y) / z) * 60.0;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = ((x - y) * 60.0d0) / (z - t)
    if (t_1 <= (-1d+82)) then
        tmp = (x / (z - t)) * 60.0d0
    else if (t_1 <= 5d+123) then
        tmp = 120.0d0 * a
    else
        tmp = ((x - y) / z) * 60.0d0
    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) / (z - t);
	double tmp;
	if (t_1 <= -1e+82) {
		tmp = (x / (z - t)) * 60.0;
	} else if (t_1 <= 5e+123) {
		tmp = 120.0 * a;
	} else {
		tmp = ((x - y) / z) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_1 <= -1e+82:
		tmp = (x / (z - t)) * 60.0
	elif t_1 <= 5e+123:
		tmp = 120.0 * a
	else:
		tmp = ((x - y) / z) * 60.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+82)
		tmp = Float64(Float64(x / Float64(z - t)) * 60.0);
	elseif (t_1 <= 5e+123)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(Float64(x - y) / z) * 60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+82)
		tmp = (x / (z - t)) * 60.0;
	elseif (t_1 <= 5e+123)
		tmp = 120.0 * a;
	else
		tmp = ((x - y) / z) * 60.0;
	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] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+82], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+123], N[(120.0 * a), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.9999999999999996e81

   1. Initial program 97.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 57.6

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

   5. Applied rewrites 57.6%

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

   if -9.9999999999999996e81 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999974e123

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 71.6

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

   5. Applied rewrites 71.6%

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

   if 4.99999999999999974e123 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.2%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 88.7

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

   5. Applied rewrites 88.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 63.8%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+123}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+82}:\\ \;\;\;\;\frac{60}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+123}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -1e+82)
     (* (/ 60.0 z) (- x y))
     (if (<= t_1 5e+123) (* 120.0 a) (* (/ (- x y) z) 60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -1e+82) {
		tmp = (60.0 / z) * (x - y);
	} else if (t_1 <= 5e+123) {
		tmp = 120.0 * a;
	} else {
		tmp = ((x - y) / z) * 60.0;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = ((x - y) * 60.0d0) / (z - t)
    if (t_1 <= (-1d+82)) then
        tmp = (60.0d0 / z) * (x - y)
    else if (t_1 <= 5d+123) then
        tmp = 120.0d0 * a
    else
        tmp = ((x - y) / z) * 60.0d0
    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) / (z - t);
	double tmp;
	if (t_1 <= -1e+82) {
		tmp = (60.0 / z) * (x - y);
	} else if (t_1 <= 5e+123) {
		tmp = 120.0 * a;
	} else {
		tmp = ((x - y) / z) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_1 <= -1e+82:
		tmp = (60.0 / z) * (x - y)
	elif t_1 <= 5e+123:
		tmp = 120.0 * a
	else:
		tmp = ((x - y) / z) * 60.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+82)
		tmp = Float64(Float64(60.0 / z) * Float64(x - y));
	elseif (t_1 <= 5e+123)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(Float64(x - y) / z) * 60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+82)
		tmp = (60.0 / z) * (x - y);
	elseif (t_1 <= 5e+123)
		tmp = 120.0 * a;
	else
		tmp = ((x - y) / z) * 60.0;
	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] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+82], N[(N[(60.0 / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+123], N[(120.0 * a), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.9999999999999996e81

   1. Initial program 97.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 90.9

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

   5. Applied rewrites 90.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 56.6%

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

   if -9.9999999999999996e81 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999974e123

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 71.6

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

   5. Applied rewrites 71.6%

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

   if 4.99999999999999974e123 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.2%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 88.7

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

   5. Applied rewrites 88.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 63.8%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{+82}:\\ \;\;\;\;\frac{60}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+123}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot 60\\ t_2 := \frac{t\_1}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+82}:\\ \;\;\;\;\frac{t\_1}{z}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+123}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- x y) 60.0)) (t_2 (/ t_1 (- z t))))
   (if (<= t_2 -1e+82)
     (/ t_1 z)
     (if (<= t_2 5e+123) (* 120.0 a) (* (/ (- x y) z) 60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) * 60.0;
	double t_2 = t_1 / (z - t);
	double tmp;
	if (t_2 <= -1e+82) {
		tmp = t_1 / z;
	} else if (t_2 <= 5e+123) {
		tmp = 120.0 * a;
	} else {
		tmp = ((x - y) / z) * 60.0;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) * 60.0d0
    t_2 = t_1 / (z - t)
    if (t_2 <= (-1d+82)) then
        tmp = t_1 / z
    else if (t_2 <= 5d+123) then
        tmp = 120.0d0 * a
    else
        tmp = ((x - y) / z) * 60.0d0
    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;
	double t_2 = t_1 / (z - t);
	double tmp;
	if (t_2 <= -1e+82) {
		tmp = t_1 / z;
	} else if (t_2 <= 5e+123) {
		tmp = 120.0 * a;
	} else {
		tmp = ((x - y) / z) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - y) * 60.0
	t_2 = t_1 / (z - t)
	tmp = 0
	if t_2 <= -1e+82:
		tmp = t_1 / z
	elif t_2 <= 5e+123:
		tmp = 120.0 * a
	else:
		tmp = ((x - y) / z) * 60.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) * 60.0)
	t_2 = Float64(t_1 / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+82)
		tmp = Float64(t_1 / z);
	elseif (t_2 <= 5e+123)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(Float64(x - y) / z) * 60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - y) * 60.0;
	t_2 = t_1 / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+82)
		tmp = t_1 / z;
	elseif (t_2 <= 5e+123)
		tmp = 120.0 * a;
	else
		tmp = ((x - y) / z) * 60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+82], N[(t$95$1 / z), $MachinePrecision], If[LessEqual[t$95$2, 5e+123], N[(120.0 * a), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.9999999999999996e81

   1. Initial program 97.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 90.9

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

   5. Applied rewrites 90.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 56.5%

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

   10. Applied rewrites 56.5%

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

   if -9.9999999999999996e81 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999974e123

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 71.6

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

   5. Applied rewrites 71.6%

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

   if 4.99999999999999974e123 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.2%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 88.7

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

   5. Applied rewrites 88.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 63.8%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{+82}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+123}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z} \cdot 60\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+123}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ (- x y) z) 60.0)) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -1e+82) t_1 (if (<= t_2 5e+123) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) / z) * 60.0;
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -1e+82) {
		tmp = t_1;
	} else if (t_2 <= 5e+123) {
		tmp = 120.0 * a;
	} 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) / z) * 60.0d0
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-1d+82)) then
        tmp = t_1
    else if (t_2 <= 5d+123) then
        tmp = 120.0d0 * a
    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) / z) * 60.0;
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -1e+82) {
		tmp = t_1;
	} else if (t_2 <= 5e+123) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) / z) * 60.0
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -1e+82:
		tmp = t_1
	elif t_2 <= 5e+123:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) / z) * 60.0)
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+82)
		tmp = t_1;
	elseif (t_2 <= 5e+123)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) / z) * 60.0;
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+82)
		tmp = t_1;
	elseif (t_2 <= 5e+123)
		tmp = 120.0 * a;
	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] / z), $MachinePrecision] * 60.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+82], t$95$1, If[LessEqual[t$95$2, 5e+123], N[(120.0 * a), $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)) < -9.9999999999999996e81 or 4.99999999999999974e123 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 89.9

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

   5. Applied rewrites 89.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 59.7%

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

   if -9.9999999999999996e81 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999974e123

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 71.6

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

   5. Applied rewrites 71.6%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{+82}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+123}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-60 \cdot x}{t - z}\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+124}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* -60.0 x) (- t z))) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -1e+82) t_1 (if (<= t_2 1e+124) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 * x) / (t - z);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -1e+82) {
		tmp = t_1;
	} else if (t_2 <= 1e+124) {
		tmp = 120.0 * a;
	} 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 = ((-60.0d0) * x) / (t - z)
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-1d+82)) then
        tmp = t_1
    else if (t_2 <= 1d+124) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 * x) / (t - z);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -1e+82) {
		tmp = t_1;
	} else if (t_2 <= 1e+124) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (-60.0 * x) / (t - z)
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -1e+82:
		tmp = t_1
	elif t_2 <= 1e+124:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-60.0 * x) / Float64(t - z))
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+82)
		tmp = t_1;
	elseif (t_2 <= 1e+124)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (-60.0 * x) / (t - z);
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+82)
		tmp = t_1;
	elseif (t_2 <= 1e+124)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(-60.0 * x), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+82], t$95$1, If[LessEqual[t$95$2, 1e+124], N[(120.0 * a), $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)) < -9.9999999999999996e81 or 9.99999999999999948e123 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 97.3

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.6

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. remove-double-neg N/A

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

      3. unsub-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 55.7

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

   7. Applied rewrites 55.7%

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

   if -9.9999999999999996e81 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999948e123

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 71.2

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

   5. Applied rewrites 71.2%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{+82}:\\ \;\;\;\;\frac{-60 \cdot x}{t - z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{+124}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60 \cdot x}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-60 \cdot x}{-z}\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+124}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* -60.0 x) (- z))) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -2e+88) t_1 (if (<= t_2 1e+124) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 * x) / -z;
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+88) {
		tmp = t_1;
	} else if (t_2 <= 1e+124) {
		tmp = 120.0 * a;
	} 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 = ((-60.0d0) * x) / -z
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-2d+88)) then
        tmp = t_1
    else if (t_2 <= 1d+124) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 * x) / -z;
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+88) {
		tmp = t_1;
	} else if (t_2 <= 1e+124) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (-60.0 * x) / -z
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -2e+88:
		tmp = t_1
	elif t_2 <= 1e+124:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-60.0 * x) / Float64(-z))
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+88)
		tmp = t_1;
	elseif (t_2 <= 1e+124)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (-60.0 * x) / -z;
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e+88)
		tmp = t_1;
	elseif (t_2 <= 1e+124)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(-60.0 * x), $MachinePrecision] / (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+88], t$95$1, If[LessEqual[t$95$2, 1e+124], N[(120.0 * a), $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)) < -1.99999999999999992e88 or 9.99999999999999948e123 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 97.2

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.6

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. remove-double-neg N/A

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

      3. unsub-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 56.4

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

   7. Applied rewrites 56.4%

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

   8. Taylor expanded in t around 0

      \[\leadsto \frac{-60 \cdot x}{-1 \cdot \color{blue}{z}} \]
   9. Step-by-step derivation

   10. Applied rewrites 41.1%

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

   if -1.99999999999999992e88 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999948e123

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 70.8

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

   5. Applied rewrites 70.8%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+88}:\\ \;\;\;\;\frac{-60 \cdot x}{-z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{+124}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60 \cdot x}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot 60\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+124}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ x z) 60.0)) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -2e+88) t_1 (if (<= t_2 1e+124) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / z) * 60.0;
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+88) {
		tmp = t_1;
	} else if (t_2 <= 1e+124) {
		tmp = 120.0 * a;
	} 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 / z) * 60.0d0
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-2d+88)) then
        tmp = t_1
    else if (t_2 <= 1d+124) then
        tmp = 120.0d0 * a
    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 / z) * 60.0;
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -2e+88) {
		tmp = t_1;
	} else if (t_2 <= 1e+124) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x / z) * 60.0
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -2e+88:
		tmp = t_1
	elif t_2 <= 1e+124:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x / z) * 60.0)
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+88)
		tmp = t_1;
	elseif (t_2 <= 1e+124)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x / z) * 60.0;
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e+88)
		tmp = t_1;
	elseif (t_2 <= 1e+124)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+88], t$95$1, If[LessEqual[t$95$2, 1e+124], N[(120.0 * a), $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)) < -1.99999999999999992e88 or 9.99999999999999948e123 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.2%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 89.7

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

   5. Applied rewrites 89.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 61.1%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 41.0%

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

   if -1.99999999999999992e88 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999948e123

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 70.8

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

   5. Applied rewrites 70.8%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+88}:\\ \;\;\;\;\frac{x}{z} \cdot 60\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{+124}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot 60\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} \cdot -60\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+221}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y z) -60.0)) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -1e+162) t_1 (if (<= t_2 1e+221) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / z) * -60.0;
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -1e+162) {
		tmp = t_1;
	} else if (t_2 <= 1e+221) {
		tmp = 120.0 * a;
	} 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 / z) * (-60.0d0)
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-1d+162)) then
        tmp = t_1
    else if (t_2 <= 1d+221) then
        tmp = 120.0d0 * a
    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 / z) * -60.0;
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -1e+162) {
		tmp = t_1;
	} else if (t_2 <= 1e+221) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / z) * -60.0
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -1e+162:
		tmp = t_1
	elif t_2 <= 1e+221:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / z) * -60.0)
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+162)
		tmp = t_1;
	elseif (t_2 <= 1e+221)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / z) * -60.0;
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+162)
		tmp = t_1;
	elseif (t_2 <= 1e+221)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * -60.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+162], t$95$1, If[LessEqual[t$95$2, 1e+221], N[(120.0 * a), $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)) < -9.9999999999999994e161 or 1e221 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 95.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 97.5

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

   5. Applied rewrites 97.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 66.5%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 37.8%

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

   if -9.9999999999999994e161 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1e221

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 63.4

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

   5. Applied rewrites 63.4%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{+162}:\\ \;\;\;\;\frac{y}{z} \cdot -60\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{+221}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot -60\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+184}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{t} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -1e+106)
     (* (/ x t) -60.0)
     (if (<= t_1 5e+184) (* 120.0 a) (* (/ -60.0 t) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -1e+106) {
		tmp = (x / t) * -60.0;
	} else if (t_1 <= 5e+184) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 / t) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x - y) * 60.0d0) / (z - t)
    if (t_1 <= (-1d+106)) then
        tmp = (x / t) * (-60.0d0)
    else if (t_1 <= 5d+184) then
        tmp = 120.0d0 * a
    else
        tmp = ((-60.0d0) / t) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -1e+106) {
		tmp = (x / t) * -60.0;
	} else if (t_1 <= 5e+184) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 / t) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_1 <= -1e+106:
		tmp = (x / t) * -60.0
	elif t_1 <= 5e+184:
		tmp = 120.0 * a
	else:
		tmp = (-60.0 / t) * x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+106)
		tmp = Float64(Float64(x / t) * -60.0);
	elseif (t_1 <= 5e+184)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(-60.0 / t) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+106)
		tmp = (x / t) * -60.0;
	elseif (t_1 <= 5e+184)
		tmp = 120.0 * a;
	else
		tmp = (-60.0 / t) * x;
	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] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+106], N[(N[(x / t), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+184], N[(120.0 * a), $MachinePrecision], N[(N[(-60.0 / t), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.00000000000000009e106

   1. Initial program 97.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 97.0

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.6

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. remove-double-neg N/A

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

      3. unsub-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 56.1

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

   7. Applied rewrites 56.1%

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

   8. Taylor expanded in t around inf

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

   10. Applied rewrites 29.7%

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

   if -1.00000000000000009e106 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.9999999999999999e184

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 67.0

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

   5. Applied rewrites 67.0%

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

   if 4.9999999999999999e184 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 95.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 95.8

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.6

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. remove-double-neg N/A

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

      3. unsub-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 52.3

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

   7. Applied rewrites 52.3%

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

   8. Taylor expanded in t around inf

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

   10. Applied rewrites 33.2%

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

   12. Applied rewrites 33.3%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+184}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{t} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-60}{t} \cdot x\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+184}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ -60.0 t) x)) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -1e+106) t_1 (if (<= t_2 5e+184) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 / t) * x;
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -1e+106) {
		tmp = t_1;
	} else if (t_2 <= 5e+184) {
		tmp = 120.0 * a;
	} 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 = ((-60.0d0) / t) * x
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-1d+106)) then
        tmp = t_1
    else if (t_2 <= 5d+184) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 / t) * x;
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -1e+106) {
		tmp = t_1;
	} else if (t_2 <= 5e+184) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (-60.0 / t) * x
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -1e+106:
		tmp = t_1
	elif t_2 <= 5e+184:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-60.0 / t) * x)
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+106)
		tmp = t_1;
	elseif (t_2 <= 5e+184)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (-60.0 / t) * x;
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+106)
		tmp = t_1;
	elseif (t_2 <= 5e+184)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(-60.0 / t), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+106], t$95$1, If[LessEqual[t$95$2, 5e+184], N[(120.0 * a), $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)) < -1.00000000000000009e106 or 4.9999999999999999e184 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 96.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 96.6

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.6

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. remove-double-neg N/A

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

      3. unsub-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 54.7

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

   7. Applied rewrites 54.7%

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

   8. Taylor expanded in t around inf

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

   10. Applied rewrites 31.0%

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

   12. Applied rewrites 31.1%

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

   if -1.00000000000000009e106 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.9999999999999999e184

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 67.0

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

   5. Applied rewrites 67.0%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{+106}:\\ \;\;\;\;\frac{-60}{t} \cdot x\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+184}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{t} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 74.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5 \cdot 10^{+44}:\\ \;\;\;\;\frac{y}{z} \cdot -60 + 120 \cdot a\\ \mathbf{elif}\;120 \cdot a \leq 5 \cdot 10^{+42}:\\ \;\;\;\;\frac{x - y}{0.016666666666666666 \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* 120.0 a) -5e+44)
   (+ (* (/ y z) -60.0) (* 120.0 a))
   (if (<= (* 120.0 a) 5e+42)
     (/ (- x y) (* 0.016666666666666666 (- z t)))
     (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -5e+44) {
		tmp = ((y / z) * -60.0) + (120.0 * a);
	} else if ((120.0 * a) <= 5e+42) {
		tmp = (x - y) / (0.016666666666666666 * (z - t));
	} else {
		tmp = 120.0 * a;
	}
	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 ((120.0d0 * a) <= (-5d+44)) then
        tmp = ((y / z) * (-60.0d0)) + (120.0d0 * a)
    else if ((120.0d0 * a) <= 5d+42) then
        tmp = (x - y) / (0.016666666666666666d0 * (z - t))
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -5e+44) {
		tmp = ((y / z) * -60.0) + (120.0 * a);
	} else if ((120.0 * a) <= 5e+42) {
		tmp = (x - y) / (0.016666666666666666 * (z - t));
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (120.0 * a) <= -5e+44:
		tmp = ((y / z) * -60.0) + (120.0 * a)
	elif (120.0 * a) <= 5e+42:
		tmp = (x - y) / (0.016666666666666666 * (z - t))
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(120.0 * a) <= -5e+44)
		tmp = Float64(Float64(Float64(y / z) * -60.0) + Float64(120.0 * a));
	elseif (Float64(120.0 * a) <= 5e+42)
		tmp = Float64(Float64(x - y) / Float64(0.016666666666666666 * Float64(z - t)));
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((120.0 * a) <= -5e+44)
		tmp = ((y / z) * -60.0) + (120.0 * a);
	elseif ((120.0 * a) <= 5e+42)
		tmp = (x - y) / (0.016666666666666666 * (z - t));
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(120.0 * a), $MachinePrecision], -5e+44], N[(N[(N[(y / z), $MachinePrecision] * -60.0), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], 5e+42], N[(N[(x - y), $MachinePrecision] / N[(0.016666666666666666 * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -4.9999999999999996e44

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 78.9

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 79.4%

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

   if -4.9999999999999996e44 < (*.f64 a #s(literal 120 binary64)) < 5.00000000000000007e42

   1. Initial program 99.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 74.7

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

   5. Applied rewrites 74.7%

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

   7. Applied rewrites 74.9%

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

   if 5.00000000000000007e42 < (*.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 a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 84.5

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

   5. Applied rewrites 84.5%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5 \cdot 10^{+44}:\\ \;\;\;\;\frac{y}{z} \cdot -60 + 120 \cdot a\\ \mathbf{elif}\;120 \cdot a \leq 5 \cdot 10^{+42}:\\ \;\;\;\;\frac{x - y}{0.016666666666666666 \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 75.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -2.15 \cdot 10^{+40}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;120 \cdot a \leq 3.1 \cdot 10^{+42}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* 120.0 a) -2.15e+40)
   (* 120.0 a)
   (if (<= (* 120.0 a) 3.1e+42) (* (/ 60.0 (- z t)) (- x y)) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -2.15e+40) {
		tmp = 120.0 * a;
	} else if ((120.0 * a) <= 3.1e+42) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = 120.0 * a;
	}
	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 ((120.0d0 * a) <= (-2.15d+40)) then
        tmp = 120.0d0 * a
    else if ((120.0d0 * a) <= 3.1d+42) then
        tmp = (60.0d0 / (z - t)) * (x - y)
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -2.15e+40) {
		tmp = 120.0 * a;
	} else if ((120.0 * a) <= 3.1e+42) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (120.0 * a) <= -2.15e+40:
		tmp = 120.0 * a
	elif (120.0 * a) <= 3.1e+42:
		tmp = (60.0 / (z - t)) * (x - y)
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(120.0 * a) <= -2.15e+40)
		tmp = Float64(120.0 * a);
	elseif (Float64(120.0 * a) <= 3.1e+42)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((120.0 * a) <= -2.15e+40)
		tmp = 120.0 * a;
	elseif ((120.0 * a) <= 3.1e+42)
		tmp = (60.0 / (z - t)) * (x - y);
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(120.0 * a), $MachinePrecision], -2.15e+40], N[(120.0 * a), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], 3.1e+42], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -2.1500000000000001e40 or 3.1000000000000002e42 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.1%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 81.2

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

   5. Applied rewrites 81.2%

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

   if -2.1500000000000001e40 < (*.f64 a #s(literal 120 binary64)) < 3.1000000000000002e42

   1. Initial program 99.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 74.7

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

   5. Applied rewrites 74.7%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -2.15 \cdot 10^{+40}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;120 \cdot a \leq 3.1 \cdot 10^{+42}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 74.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{if}\;t \leq -1.12 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-287}:\\ \;\;\;\;\frac{y}{z} \cdot -60 + 120 \cdot a\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{z} \cdot 60\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x y) t) -60.0 (* 120.0 a))))
   (if (<= t -1.12e-6)
     t_1
     (if (<= t 2.1e-287)
       (+ (* (/ y z) -60.0) (* 120.0 a))
       (if (<= t 1.9e-10) (fma a 120.0 (* (/ x z) 60.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((x - y) / t), -60.0, (120.0 * a));
	double tmp;
	if (t <= -1.12e-6) {
		tmp = t_1;
	} else if (t <= 2.1e-287) {
		tmp = ((y / z) * -60.0) + (120.0 * a);
	} else if (t <= 1.9e-10) {
		tmp = fma(a, 120.0, ((x / z) * 60.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(x - y) / t), -60.0, Float64(120.0 * a))
	tmp = 0.0
	if (t <= -1.12e-6)
		tmp = t_1;
	elseif (t <= 2.1e-287)
		tmp = Float64(Float64(Float64(y / z) * -60.0) + Float64(120.0 * a));
	elseif (t <= 1.9e-10)
		tmp = fma(a, 120.0, Float64(Float64(x / z) * 60.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.12e-6], t$95$1, If[LessEqual[t, 2.1e-287], N[(N[(N[(y / z), $MachinePrecision] * -60.0), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-10], N[(a * 120.0 + N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.12000000000000008e-6 or 1.8999999999999999e-10 < t

   1. Initial program 99.1%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 91.8

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

   5. Applied rewrites 91.8%

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

   if -1.12000000000000008e-6 < t < 2.0999999999999999e-287

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 84.7

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

   5. Applied rewrites 84.7%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 70.1%

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

   if 2.0999999999999999e-287 < t < 1.8999999999999999e-10

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 87.3

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

   5. Applied rewrites 87.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 74.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 74.8

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

   10. Applied rewrites 74.8%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-287}:\\ \;\;\;\;\frac{y}{z} \cdot -60 + 120 \cdot a\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{z} \cdot 60\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 89.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{-60 \cdot y}{z - t}\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+70}:\\ \;\;\;\;\frac{x \cdot 60}{z - t} + 120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{-60}{z - t} \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.2e+56)
   (fma a 120.0 (/ (* -60.0 y) (- z t)))
   (if (<= y 3.8e+70)
     (+ (/ (* x 60.0) (- z t)) (* 120.0 a))
     (fma a 120.0 (* (/ -60.0 (- z t)) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.2e+56) {
		tmp = fma(a, 120.0, ((-60.0 * y) / (z - t)));
	} else if (y <= 3.8e+70) {
		tmp = ((x * 60.0) / (z - t)) + (120.0 * a);
	} else {
		tmp = fma(a, 120.0, ((-60.0 / (z - t)) * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.2e+56)
		tmp = fma(a, 120.0, Float64(Float64(-60.0 * y) / Float64(z - t)));
	elseif (y <= 3.8e+70)
		tmp = Float64(Float64(Float64(x * 60.0) / Float64(z - t)) + Float64(120.0 * a));
	else
		tmp = fma(a, 120.0, Float64(Float64(-60.0 / Float64(z - t)) * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.2e+56], N[(a * 120.0 + N[(N[(-60.0 * y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+70], N[(N[(N[(x * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(a * 120.0 + N[(N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.20000000000000034e56

   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. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. distribute-lft-in N/A

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

      6. neg-mul-1 N/A

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

      7. associate-*r* N/A

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

      8. metadata-eval N/A

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

      9. metadata-eval N/A

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

      10. lower-fma.f64 N/A

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

      11. metadata-eval N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.8

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

      5. lift-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 99.8

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 99.8

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 88.3

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

   9. Applied rewrites 88.3%

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

   if -4.20000000000000034e56 < y < 3.7999999999999998e70

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 95.8

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

   5. Applied rewrites 95.8%

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

   if 3.7999999999999998e70 < y

   1. Initial program 96.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 96.6

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.6

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. associate-*l/ N/A

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

      3. remove-double-neg N/A

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

      4. unsub-neg N/A

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

      5. distribute-neg-in N/A

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

      6. +-commutative N/A

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

      7. sub-neg N/A

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

      8. distribute-neg-frac2 N/A

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

      9. metadata-eval N/A

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

      10. associate-*r/ N/A

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

      11. lower-*.f64 N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. distribute-neg-frac N/A

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

      15. metadata-eval N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 93.0

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

   7. Applied rewrites 93.0%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{-60 \cdot y}{z - t}\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+70}:\\ \;\;\;\;\frac{x \cdot 60}{z - t} + 120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{-60}{z - t} \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{t}\\ \mathbf{if}\;t \leq -23500:\\ \;\;\;\;\mathsf{fma}\left(a, 120, t\_1 \cdot -60\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-7}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60 + 120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, -60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x y) t)))
   (if (<= t -23500.0)
     (fma a 120.0 (* t_1 -60.0))
     (if (<= t 2e-7)
       (+ (* (/ (- x y) z) 60.0) (* 120.0 a))
       (fma t_1 -60.0 (* 120.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) / t;
	double tmp;
	if (t <= -23500.0) {
		tmp = fma(a, 120.0, (t_1 * -60.0));
	} else if (t <= 2e-7) {
		tmp = (((x - y) / z) * 60.0) + (120.0 * a);
	} else {
		tmp = fma(t_1, -60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) / t)
	tmp = 0.0
	if (t <= -23500.0)
		tmp = fma(a, 120.0, Float64(t_1 * -60.0));
	elseif (t <= 2e-7)
		tmp = Float64(Float64(Float64(Float64(x - y) / z) * 60.0) + Float64(120.0 * a));
	else
		tmp = fma(t_1, -60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -23500.0], N[(a * 120.0 + N[(t$95$1 * -60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e-7], N[(N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -23500

   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. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.9

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 93.5

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

   7. Applied rewrites 93.5%

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

   if -23500 < t < 1.9999999999999999e-7

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 85.7

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

   5. Applied rewrites 85.7%

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

   if 1.9999999999999999e-7 < t

   1. Initial program 98.4%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 92.8

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

   5. Applied rewrites 92.8%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -23500:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{t} \cdot -60\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-7}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60 + 120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{t}\\ \mathbf{if}\;t \leq -23500:\\ \;\;\;\;\mathsf{fma}\left(a, 120, t\_1 \cdot -60\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, -60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x y) t)))
   (if (<= t -23500.0)
     (fma a 120.0 (* t_1 -60.0))
     (if (<= t 2e-7)
       (fma (/ (- x y) z) 60.0 (* 120.0 a))
       (fma t_1 -60.0 (* 120.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) / t;
	double tmp;
	if (t <= -23500.0) {
		tmp = fma(a, 120.0, (t_1 * -60.0));
	} else if (t <= 2e-7) {
		tmp = fma(((x - y) / z), 60.0, (120.0 * a));
	} else {
		tmp = fma(t_1, -60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) / t)
	tmp = 0.0
	if (t <= -23500.0)
		tmp = fma(a, 120.0, Float64(t_1 * -60.0));
	elseif (t <= 2e-7)
		tmp = fma(Float64(Float64(x - y) / z), 60.0, Float64(120.0 * a));
	else
		tmp = fma(t_1, -60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -23500.0], N[(a * 120.0 + N[(t$95$1 * -60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e-7], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -23500

   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. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.9

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 93.5

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

   7. Applied rewrites 93.5%

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

   if -23500 < t < 1.9999999999999999e-7

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 85.6

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

   5. Applied rewrites 85.6%

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

   if 1.9999999999999999e-7 < t

   1. Initial program 98.4%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 92.8

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

   5. Applied rewrites 92.8%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -23500:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{t} \cdot -60\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{if}\;t \leq -23500:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x y) t) -60.0 (* 120.0 a))))
   (if (<= t -23500.0)
     t_1
     (if (<= t 2e-7) (fma (/ (- x y) z) 60.0 (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((x - y) / t), -60.0, (120.0 * a));
	double tmp;
	if (t <= -23500.0) {
		tmp = t_1;
	} else if (t <= 2e-7) {
		tmp = fma(((x - y) / z), 60.0, (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(x - y) / t), -60.0, Float64(120.0 * a))
	tmp = 0.0
	if (t <= -23500.0)
		tmp = t_1;
	elseif (t <= 2e-7)
		tmp = fma(Float64(Float64(x - y) / z), 60.0, Float64(120.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -23500.0], t$95$1, If[LessEqual[t, 2e-7], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -23500 or 1.9999999999999999e-7 < t

   1. Initial program 99.1%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 93.1

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

   5. Applied rewrites 93.1%

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

   if -23500 < t < 1.9999999999999999e-7

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 85.6

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

   5. Applied rewrites 85.6%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -23500:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 99.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 99.1

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

   5. lift-/.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. *-commutative N/A

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

   8. associate-/l* N/A

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

   9. *-commutative N/A

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

   10. lower-*.f64 N/A

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

   11. frac-2neg N/A

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

   12. lower-/.f64 N/A

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

   13. metadata-eval N/A

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

   14. neg-sub0 N/A

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

   15. lift--.f64 N/A

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

   16. sub-neg N/A

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

   17. +-commutative N/A

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

   18. associate--r+ N/A

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

   19. neg-sub0 N/A

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

   20. remove-double-neg N/A

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

   21. lower--.f64 99.8

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

4. Applied rewrites 99.8%

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

Alternative 22: 50.6% accurate, 5.2× speedup

Math

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

FPCore

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

C

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

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 = 120.0d0 * a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

3. Taylor expanded in a around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 52.6

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

5. Applied rewrites 52.6%

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

6. Final simplification 52.6%

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

Developer Target 1: 99.8% 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 2024235 
(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)))