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

Percentage Accurate: 99.3% → 99.8%

Time: 10.7s

Alternatives: 17

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: 99.3% 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 98.7%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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: 73.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t} \cdot \left(x - y\right)\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -0.02:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-40}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;t\_2 \leq 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+130}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ 60.0 (- z t)) (- x y))) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -0.02)
     t_1
     (if (<= t_2 5e-40)
       (* 120.0 a)
       (if (<= t_2 1e+40)
         t_1
         (if (<= t_2 5e+130) (fma (/ y t) 60.0 (* 120.0 a)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / (z - t)) * (x - y);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -0.02) {
		tmp = t_1;
	} else if (t_2 <= 5e-40) {
		tmp = 120.0 * a;
	} else if (t_2 <= 1e+40) {
		tmp = t_1;
	} else if (t_2 <= 5e+130) {
		tmp = fma((y / t), 60.0, (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y))
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -0.02)
		tmp = t_1;
	elseif (t_2 <= 5e-40)
		tmp = Float64(120.0 * a);
	elseif (t_2 <= 1e+40)
		tmp = t_1;
	elseif (t_2 <= 5e+130)
		tmp = fma(Float64(y / t), 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[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $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, -0.02], t$95$1, If[LessEqual[t$95$2, 5e-40], N[(120.0 * a), $MachinePrecision], If[LessEqual[t$95$2, 1e+40], t$95$1, If[LessEqual[t$95$2, 5e+130], N[(N[(y / t), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -0.0200000000000000004 or 4.99999999999999965e-40 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.00000000000000003e40 or 4.9999999999999996e130 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   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 80.3

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

   5. Applied rewrites 80.3%

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

   if -0.0200000000000000004 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999965e-40

   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 81.0

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

   5. Applied rewrites 81.0%

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

   if 1.00000000000000003e40 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.9999999999999996e130

   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 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 71.0

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

   5. Applied rewrites 71.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 80.9%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -0.02:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{-40}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{+40}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+130}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+127}:\\ \;\;\;\;\frac{x - y}{t} \cdot -60\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+138}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -4e+127)
     (* (/ (- x y) t) -60.0)
     (if (<= t_1 2e+138) (* 120.0 a) (* (/ 60.0 (- z 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 <= -4e+127) {
		tmp = ((x - y) / t) * -60.0;
	} else if (t_1 <= 2e+138) {
		tmp = 120.0 * a;
	} else {
		tmp = (60.0 / (z - t)) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x - y) * 60.0d0) / (z - t)
    if (t_1 <= (-4d+127)) then
        tmp = ((x - y) / t) * (-60.0d0)
    else if (t_1 <= 2d+138) then
        tmp = 120.0d0 * a
    else
        tmp = (60.0d0 / (z - t)) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -4e+127) {
		tmp = ((x - y) / t) * -60.0;
	} else if (t_1 <= 2e+138) {
		tmp = 120.0 * a;
	} else {
		tmp = (60.0 / (z - 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 <= -4e+127:
		tmp = ((x - y) / t) * -60.0
	elif t_1 <= 2e+138:
		tmp = 120.0 * a
	else:
		tmp = (60.0 / (z - 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 <= -4e+127)
		tmp = Float64(Float64(Float64(x - y) / t) * -60.0);
	elseif (t_1 <= 2e+138)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(60.0 / Float64(z - 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 <= -4e+127)
		tmp = ((x - y) / t) * -60.0;
	elseif (t_1 <= 2e+138)
		tmp = 120.0 * a;
	else
		tmp = (60.0 / (z - 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, -4e+127], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+138], N[(120.0 * a), $MachinePrecision], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -3.99999999999999982e127

   1. Initial program 97.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 58.7

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

   5. Applied rewrites 58.7%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 54.6%

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

   if -3.99999999999999982e127 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.0000000000000001e138

   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 69.1

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

   5. Applied rewrites 69.1%

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

   if 2.0000000000000001e138 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 94.9%

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

   3. Taylor expanded in x around inf

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

      1. *-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 57.4

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

   5. Applied rewrites 57.4%

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

   7. Applied rewrites 57.4%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -4 \cdot 10^{+127}:\\ \;\;\;\;\frac{x - y}{t} \cdot -60\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+138}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+127}:\\ \;\;\;\;\frac{x - y}{t} \cdot -60\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+130}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -4e+127)
     (* (/ (- x y) t) -60.0)
     (if (<= t_1 5e+130) (* 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 <= -4e+127) {
		tmp = ((x - y) / t) * -60.0;
	} else if (t_1 <= 5e+130) {
		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 <= (-4d+127)) then
        tmp = ((x - y) / t) * (-60.0d0)
    else if (t_1 <= 5d+130) 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 <= -4e+127) {
		tmp = ((x - y) / t) * -60.0;
	} else if (t_1 <= 5e+130) {
		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 <= -4e+127:
		tmp = ((x - y) / t) * -60.0
	elif t_1 <= 5e+130:
		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 <= -4e+127)
		tmp = Float64(Float64(Float64(x - y) / t) * -60.0);
	elseif (t_1 <= 5e+130)
		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 <= -4e+127)
		tmp = ((x - y) / t) * -60.0;
	elseif (t_1 <= 5e+130)
		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, -4e+127], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+130], 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)) < -3.99999999999999982e127

   1. Initial program 97.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 58.7

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

   5. Applied rewrites 58.7%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 54.6%

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

   if -3.99999999999999982e127 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.9999999999999996e130

   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 69.6

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

   5. Applied rewrites 69.6%

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

   if 4.9999999999999996e130 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 95.2%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 55.4

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

   5. Applied rewrites 55.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 50.9%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -4 \cdot 10^{+127}:\\ \;\;\;\;\frac{x - y}{t} \cdot -60\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+130}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{t} \cdot -60\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+160}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ (- x y) t) -60.0)) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -4e+127) t_1 (if (<= t_2 2e+160) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) / t) * -60.0;
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -4e+127) {
		tmp = t_1;
	} else if (t_2 <= 2e+160) {
		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) / t) * (-60.0d0)
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-4d+127)) then
        tmp = t_1
    else if (t_2 <= 2d+160) 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) / t) * -60.0;
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -4e+127) {
		tmp = t_1;
	} else if (t_2 <= 2e+160) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) / t) * -60.0
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -4e+127:
		tmp = t_1
	elif t_2 <= 2e+160:
		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) / t) * -60.0)
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -4e+127)
		tmp = t_1;
	elseif (t_2 <= 2e+160)
		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) / t) * -60.0;
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -4e+127)
		tmp = t_1;
	elseif (t_2 <= 2e+160)
		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] / t), $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, -4e+127], t$95$1, If[LessEqual[t$95$2, 2e+160], 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)) < -3.99999999999999982e127 or 2.00000000000000001e160 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 95.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 60.7

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

   5. Applied rewrites 60.7%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 55.4%

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

   if -3.99999999999999982e127 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.00000000000000001e160

   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 66.7

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

   5. Applied rewrites 66.7%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -4 \cdot 10^{+127}:\\ \;\;\;\;\frac{x - y}{t} \cdot -60\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+160}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{t} \cdot -60\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-60}{t} \cdot \left(x - y\right)\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+160}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ -60.0 t) (- x y))) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -4e+127) t_1 (if (<= t_2 2e+160) (* 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 - y);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -4e+127) {
		tmp = t_1;
	} else if (t_2 <= 2e+160) {
		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 - y)
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-4d+127)) then
        tmp = t_1
    else if (t_2 <= 2d+160) 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 - y);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -4e+127) {
		tmp = t_1;
	} else if (t_2 <= 2e+160) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (-60.0 / t) * (x - y)
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -4e+127:
		tmp = t_1
	elif t_2 <= 2e+160:
		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) * Float64(x - y))
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -4e+127)
		tmp = t_1;
	elseif (t_2 <= 2e+160)
		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 - y);
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -4e+127)
		tmp = t_1;
	elseif (t_2 <= 2e+160)
		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] * N[(x - y), $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, -4e+127], t$95$1, If[LessEqual[t$95$2, 2e+160], 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)) < -3.99999999999999982e127 or 2.00000000000000001e160 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 95.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 60.7

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

   5. Applied rewrites 60.7%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 55.4%

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

   10. Applied rewrites 55.3%

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

   if -3.99999999999999982e127 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.00000000000000001e160

   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 66.7

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

   5. Applied rewrites 66.7%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -4 \cdot 10^{+127}:\\ \;\;\;\;\frac{-60}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+160}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{t} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+127}:\\ \;\;\;\;\frac{y \cdot 60}{t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+160}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -4e+127)
     (/ (* y 60.0) t)
     (if (<= t_1 2e+160) (* 120.0 a) (* (/ x t) -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 <= -4e+127) {
		tmp = (y * 60.0) / t;
	} else if (t_1 <= 2e+160) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / t) * -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 <= (-4d+127)) then
        tmp = (y * 60.0d0) / t
    else if (t_1 <= 2d+160) then
        tmp = 120.0d0 * a
    else
        tmp = (x / t) * (-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 <= -4e+127) {
		tmp = (y * 60.0) / t;
	} else if (t_1 <= 2e+160) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / t) * -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 <= -4e+127:
		tmp = (y * 60.0) / t
	elif t_1 <= 2e+160:
		tmp = 120.0 * a
	else:
		tmp = (x / t) * -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 <= -4e+127)
		tmp = Float64(Float64(y * 60.0) / t);
	elseif (t_1 <= 2e+160)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x / t) * -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 <= -4e+127)
		tmp = (y * 60.0) / t;
	elseif (t_1 <= 2e+160)
		tmp = 120.0 * a;
	else
		tmp = (x / t) * -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, -4e+127], N[(N[(y * 60.0), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 2e+160], N[(120.0 * a), $MachinePrecision], N[(N[(x / t), $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)) < -3.99999999999999982e127

   1. Initial program 97.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 58.7

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

   5. Applied rewrites 58.7%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 31.1%

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

   10. Applied rewrites 31.2%

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

   if -3.99999999999999982e127 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.00000000000000001e160

   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 66.7

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

   5. Applied rewrites 66.7%

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

   if 2.00000000000000001e160 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 93.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 63.4

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

   5. Applied rewrites 63.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 43.6%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -4 \cdot 10^{+127}:\\ \;\;\;\;\frac{y \cdot 60}{t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+160}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+127}:\\ \;\;\;\;\frac{y}{t} \cdot 60\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+160}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -4e+127)
     (* (/ y t) 60.0)
     (if (<= t_1 2e+160) (* 120.0 a) (* (/ x t) -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 <= -4e+127) {
		tmp = (y / t) * 60.0;
	} else if (t_1 <= 2e+160) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / t) * -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 <= (-4d+127)) then
        tmp = (y / t) * 60.0d0
    else if (t_1 <= 2d+160) then
        tmp = 120.0d0 * a
    else
        tmp = (x / t) * (-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 <= -4e+127) {
		tmp = (y / t) * 60.0;
	} else if (t_1 <= 2e+160) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / t) * -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 <= -4e+127:
		tmp = (y / t) * 60.0
	elif t_1 <= 2e+160:
		tmp = 120.0 * a
	else:
		tmp = (x / t) * -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 <= -4e+127)
		tmp = Float64(Float64(y / t) * 60.0);
	elseif (t_1 <= 2e+160)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x / t) * -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 <= -4e+127)
		tmp = (y / t) * 60.0;
	elseif (t_1 <= 2e+160)
		tmp = 120.0 * a;
	else
		tmp = (x / t) * -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, -4e+127], N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+160], N[(120.0 * a), $MachinePrecision], N[(N[(x / t), $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)) < -3.99999999999999982e127

   1. Initial program 97.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 58.7

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

   5. Applied rewrites 58.7%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 31.1%

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

   if -3.99999999999999982e127 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.00000000000000001e160

   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 66.7

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

   5. Applied rewrites 66.7%

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

   if 2.00000000000000001e160 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 93.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 63.4

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

   5. Applied rewrites 63.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 43.6%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -4 \cdot 10^{+127}:\\ \;\;\;\;\frac{y}{t} \cdot 60\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+160}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+127}:\\ \;\;\;\;\frac{60}{t} \cdot y\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+160}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -4e+127)
     (* (/ 60.0 t) y)
     (if (<= t_1 2e+160) (* 120.0 a) (* (/ x t) -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 <= -4e+127) {
		tmp = (60.0 / t) * y;
	} else if (t_1 <= 2e+160) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / t) * -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 <= (-4d+127)) then
        tmp = (60.0d0 / t) * y
    else if (t_1 <= 2d+160) then
        tmp = 120.0d0 * a
    else
        tmp = (x / t) * (-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 <= -4e+127) {
		tmp = (60.0 / t) * y;
	} else if (t_1 <= 2e+160) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / t) * -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 <= -4e+127:
		tmp = (60.0 / t) * y
	elif t_1 <= 2e+160:
		tmp = 120.0 * a
	else:
		tmp = (x / t) * -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 <= -4e+127)
		tmp = Float64(Float64(60.0 / t) * y);
	elseif (t_1 <= 2e+160)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x / t) * -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 <= -4e+127)
		tmp = (60.0 / t) * y;
	elseif (t_1 <= 2e+160)
		tmp = 120.0 * a;
	else
		tmp = (x / t) * -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, -4e+127], N[(N[(60.0 / t), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 2e+160], N[(120.0 * a), $MachinePrecision], N[(N[(x / t), $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)) < -3.99999999999999982e127

   1. Initial program 97.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 58.7

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

   5. Applied rewrites 58.7%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 31.1%

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

   10. Applied rewrites 31.1%

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

   if -3.99999999999999982e127 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.00000000000000001e160

   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 66.7

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

   5. Applied rewrites 66.7%

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

   if 2.00000000000000001e160 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 93.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 63.4

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

   5. Applied rewrites 63.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 43.6%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -4 \cdot 10^{+127}:\\ \;\;\;\;\frac{60}{t} \cdot y\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+160}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{t} \cdot y\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+227}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ 60.0 t) y)) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -4e+127) t_1 (if (<= t_2 5e+227) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / t) * y;
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -4e+127) {
		tmp = t_1;
	} else if (t_2 <= 5e+227) {
		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) * y
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-4d+127)) then
        tmp = t_1
    else if (t_2 <= 5d+227) 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) * y;
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -4e+127) {
		tmp = t_1;
	} else if (t_2 <= 5e+227) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 / t) * y
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -4e+127:
		tmp = t_1
	elif t_2 <= 5e+227:
		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) * y)
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -4e+127)
		tmp = t_1;
	elseif (t_2 <= 5e+227)
		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) * y;
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -4e+127)
		tmp = t_1;
	elseif (t_2 <= 5e+227)
		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] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+127], t$95$1, If[LessEqual[t$95$2, 5e+227], 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)) < -3.99999999999999982e127 or 4.9999999999999996e227 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 94.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 59.9

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

   5. Applied rewrites 59.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 29.2%

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

   10. Applied rewrites 29.1%

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

   if -3.99999999999999982e127 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.9999999999999996e227

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 64.2

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

   5. Applied rewrites 64.2%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -4 \cdot 10^{+127}:\\ \;\;\;\;\frac{60}{t} \cdot y\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+227}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{t} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;z \leq -7.3 \cdot 10^{-68}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z}, -60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e+21)
   (fma (/ x z) 60.0 (* 120.0 a))
   (if (<= z -7.3e-68)
     (* (/ 60.0 (- z t)) (- x y))
     (if (<= z 1.4e-38)
       (fma (/ (- x y) t) -60.0 (* 120.0 a))
       (fma (/ y z) -60.0 (* 120.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+21) {
		tmp = fma((x / z), 60.0, (120.0 * a));
	} else if (z <= -7.3e-68) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if (z <= 1.4e-38) {
		tmp = fma(((x - y) / t), -60.0, (120.0 * a));
	} else {
		tmp = fma((y / z), -60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e+21)
		tmp = fma(Float64(x / z), 60.0, Float64(120.0 * a));
	elseif (z <= -7.3e-68)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	elseif (z <= 1.4e-38)
		tmp = fma(Float64(Float64(x - y) / t), -60.0, Float64(120.0 * a));
	else
		tmp = fma(Float64(y / z), -60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e+21], N[(N[(x / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.3e-68], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-38], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.5e21

   1. Initial program 98.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 91.7

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

   5. Applied rewrites 91.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 80.4%

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

   if -4.5e21 < z < -7.30000000000000009e-68

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-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 78.8

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

   5. Applied rewrites 78.8%

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

   if -7.30000000000000009e-68 < z < 1.4e-38

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 86.3

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

   5. Applied rewrites 86.3%

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

   if 1.4e-38 < z

   1. Initial program 97.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 84.3

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

   5. Applied rewrites 84.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 75.7%

      \[\leadsto \mathsf{fma}\left(\frac{y}{z}, \color{blue}{-60}, a \cdot 120\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;z \leq -7.3 \cdot 10^{-68}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z}, -60, 120 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;z \leq -7.3 \cdot 10^{-68}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{t} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z}, -60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e+21)
   (fma (/ x z) 60.0 (* 120.0 a))
   (if (<= z -7.3e-68)
     (* (/ 60.0 (- z t)) (- x y))
     (if (<= z 1.4e-38)
       (fma a 120.0 (* (/ (- x y) t) -60.0))
       (fma (/ y z) -60.0 (* 120.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+21) {
		tmp = fma((x / z), 60.0, (120.0 * a));
	} else if (z <= -7.3e-68) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if (z <= 1.4e-38) {
		tmp = fma(a, 120.0, (((x - y) / t) * -60.0));
	} else {
		tmp = fma((y / z), -60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e+21)
		tmp = fma(Float64(x / z), 60.0, Float64(120.0 * a));
	elseif (z <= -7.3e-68)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	elseif (z <= 1.4e-38)
		tmp = fma(a, 120.0, Float64(Float64(Float64(x - y) / t) * -60.0));
	else
		tmp = fma(Float64(y / z), -60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e+21], N[(N[(x / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.3e-68], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-38], N[(a * 120.0 + N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.5e21

   1. Initial program 98.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 91.7

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

   5. Applied rewrites 91.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 80.4%

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

   if -4.5e21 < z < -7.30000000000000009e-68

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-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 78.8

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

   5. Applied rewrites 78.8%

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

   if -7.30000000000000009e-68 < z < 1.4e-38

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 86.3

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

   5. Applied rewrites 86.3%

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

   7. Applied rewrites 86.3%

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

   if 1.4e-38 < z

   1. Initial program 97.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 84.3

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

   5. Applied rewrites 84.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 75.7%

      \[\leadsto \mathsf{fma}\left(\frac{y}{z}, \color{blue}{-60}, a \cdot 120\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;z \leq -7.3 \cdot 10^{-68}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{t} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z}, -60, 120 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 89.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot 60}{z - t} + 120 \cdot a\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{-60 \cdot y}{z - t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (/ (* x 60.0) (- z t)) (* 120.0 a))))
   (if (<= x -2.15e+40)
     t_1
     (if (<= x 5.3e-11) (fma a 120.0 (/ (* -60.0 y) (- z t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x * 60.0) / (z - t)) + (120.0 * a);
	double tmp;
	if (x <= -2.15e+40) {
		tmp = t_1;
	} else if (x <= 5.3e-11) {
		tmp = fma(a, 120.0, ((-60.0 * y) / (z - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x * 60.0) / Float64(z - t)) + Float64(120.0 * a))
	tmp = 0.0
	if (x <= -2.15e+40)
		tmp = t_1;
	elseif (x <= 5.3e-11)
		tmp = fma(a, 120.0, Float64(Float64(-60.0 * y) / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.15e+40], t$95$1, If[LessEqual[x, 5.3e-11], N[(a * 120.0 + N[(N[(-60.0 * y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1500000000000001e40 or 5.2999999999999998e-11 < x

   1. Initial program 97.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 88.6

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

   5. Applied rewrites 88.6%

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

   if -2.1500000000000001e40 < x < 5.2999999999999998e-11

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 92.0

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

   5. Applied rewrites 92.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 92.0

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

   7. Applied rewrites 92.0%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+40}:\\ \;\;\;\;\frac{x \cdot 60}{z - t} + 120 \cdot a\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{-60 \cdot y}{z - t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 60}{z - t} + 120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{t}\\ \mathbf{if}\;t \leq -1.36 \cdot 10^{-74}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, -60, 120 \cdot a\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-53}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, t\_1 \cdot -60\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x y) t)))
   (if (<= t -1.36e-74)
     (fma t_1 -60.0 (* 120.0 a))
     (if (<= t 2.7e-53)
       (fma (/ (- x y) z) 60.0 (* 120.0 a))
       (fma a 120.0 (* t_1 -60.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) / t;
	double tmp;
	if (t <= -1.36e-74) {
		tmp = fma(t_1, -60.0, (120.0 * a));
	} else if (t <= 2.7e-53) {
		tmp = fma(((x - y) / z), 60.0, (120.0 * a));
	} else {
		tmp = fma(a, 120.0, (t_1 * -60.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) / t)
	tmp = 0.0
	if (t <= -1.36e-74)
		tmp = fma(t_1, -60.0, Float64(120.0 * a));
	elseif (t <= 2.7e-53)
		tmp = fma(Float64(Float64(x - y) / z), 60.0, Float64(120.0 * a));
	else
		tmp = fma(a, 120.0, Float64(t_1 * -60.0));
	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, -1.36e-74], N[(t$95$1 * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e-53], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(a * 120.0 + N[(t$95$1 * -60.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.36000000000000006e-74

   1. Initial program 97.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 83.1

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

   5. Applied rewrites 83.1%

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

   if -1.36000000000000006e-74 < t < 2.6999999999999999e-53

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 86.6

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

   5. Applied rewrites 86.6%

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

   if 2.6999999999999999e-53 < t

   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 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 89.2

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

   5. Applied rewrites 89.2%

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

   7. Applied rewrites 89.3%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{-74}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-53}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{t} \cdot -60\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 66.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{z}, -60, 120 \cdot a\right)\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y z) -60.0 (* 120.0 a))))
   (if (<= z -8.2e-15)
     t_1
     (if (<= z 3.6e-39) (fma (/ y t) 60.0 (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / z), -60.0, (120.0 * a));
	double tmp;
	if (z <= -8.2e-15) {
		tmp = t_1;
	} else if (z <= 3.6e-39) {
		tmp = fma((y / t), 60.0, (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y / z), -60.0, Float64(120.0 * a))
	tmp = 0.0
	if (z <= -8.2e-15)
		tmp = t_1;
	elseif (z <= 3.6e-39)
		tmp = fma(Float64(y / t), 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[(y / z), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e-15], t$95$1, If[LessEqual[z, 3.6e-39], N[(N[(y / t), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.20000000000000072e-15 or 3.6000000000000001e-39 < z

   1. Initial program 97.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 87.7

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

   5. Applied rewrites 87.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 75.7%

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

   if -8.20000000000000072e-15 < z < 3.6000000000000001e-39

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 83.1

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

   5. Applied rewrites 83.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 62.0%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-15}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z}, -60, 120 \cdot a\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z}, -60, 120 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 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 98.7%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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 98.7

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

   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 17: 50.7% 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 98.7%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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 51.7

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

5. Applied rewrites 51.7%

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

6. Final simplification 51.7%

   \[\leadsto 120 \cdot a \]
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 2024268 
(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)))