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

Percentage Accurate: 99.4% → 99.8%

Time: 12.3s

Alternatives: 22

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(a, 120, \frac{x - y}{-0.016666666666666666 \cdot \left(t - z\right)}\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (fma a 120.0 (/ (- x y) (* -0.016666666666666666 (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	return fma(a, 120.0, ((x - y) / (-0.016666666666666666 * (t - z))));
}

Julia

function code(x, y, z, t, a)
	return fma(a, 120.0, Float64(Float64(x - y) / Float64(-0.016666666666666666 * Float64(t - z))))
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(a * 120.0 + N[(N[(x - y), $MachinePrecision] / N[(-0.016666666666666666 * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.1%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 99.1

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

   5. lift-/.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. *-commutative N/A

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

   8. associate-/l* N/A

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

   9. *-commutative N/A

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

   10. lower-*.f64 N/A

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

   11. frac-2neg N/A

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

   12. lower-/.f64 N/A

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

   13. metadata-eval N/A

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

   14. neg-sub0 N/A

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

   15. lift--.f64 N/A

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

   16. sub-neg N/A

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

   17. +-commutative N/A

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

   18. associate--r+ N/A

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

   19. neg-sub0 N/A

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

   20. remove-double-neg N/A

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

   21. lower--.f64 99.8

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

4. Applied rewrites 99.8%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. clear-num N/A

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

   5. un-div-inv N/A

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

   6. lower-/.f64 N/A

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

   7. div-inv N/A

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

   8. lower-*.f64 N/A

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

   9. metadata-eval 99.9

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

6. Applied rewrites 99.9%

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

7. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(a, 120, \frac{x - y}{-0.016666666666666666 \cdot \left(t - z\right)}\right) \]
8. Add Preprocessing

Alternative 2: 83.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{0.016666666666666666 \cdot \left(z - t\right)}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t - z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x y) (* 0.016666666666666666 (- z t))))
        (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -2e+88)
     t_1
     (if (<= t_2 5e+123) (fma (/ y (- t z)) 60.0 (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) / (0.016666666666666666 * (z - t));
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+88) {
		tmp = t_1;
	} else if (t_2 <= 5e+123) {
		tmp = fma((y / (t - z)), 60.0, (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) / Float64(0.016666666666666666 * Float64(z - t)))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+88)
		tmp = t_1;
	elseif (t_2 <= 5e+123)
		tmp = fma(Float64(y / Float64(t - z)), 60.0, Float64(120.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(0.016666666666666666 * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+88], t$95$1, If[LessEqual[t$95$2, 5e+123], N[(N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.99999999999999992e88 or 4.99999999999999974e123 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.3%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 89.8

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

   5. Applied rewrites 89.8%

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

   7. Applied rewrites 87.4%

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

   9. Applied rewrites 90.0%

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

   if -1.99999999999999992e88 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999974e123

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.9

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 87.1

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

   7. Applied rewrites 87.1%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{+88}:\\ \;\;\;\;\frac{x - y}{0.016666666666666666 \cdot \left(z - t\right)}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t - z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{0.016666666666666666 \cdot \left(z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.7% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (0.016666666666666666d0 * (z - t))
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-2d+39)) then
        tmp = t_1
    else if (t_2 <= 5d-27) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(0.016666666666666666 * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+39], t$95$1, If[LessEqual[t$95$2, 5e-27], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 98.1%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 77.6

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

   5. Applied rewrites 77.6%

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

   7. Applied rewrites 76.1%

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

   9. Applied rewrites 77.7%

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

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

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 78.2

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

   5. Applied rewrites 78.2%

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

4. Final simplification 78.0%

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

Alternative 4: 74.7% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

   1. Initial program 97.8%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 84.2

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

   5. Applied rewrites 84.2%

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

   7. Applied rewrites 84.3%

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

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

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 78.2

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

   5. Applied rewrites 78.2%

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

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

   1. Initial program 98.4%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 72.1

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

   5. Applied rewrites 72.1%

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

4. Final simplification 77.9%

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

Alternative 5: 60.2% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+82)
		tmp = x / (0.016666666666666666 * (z - t));
	elseif (t_1 <= 5e+123)
		tmp = 120.0 * a;
	else
		tmp = ((x - y) / z) * 60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+82], N[(x / N[(0.016666666666666666 * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+123], N[(120.0 * a), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 57.6

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

   5. Applied rewrites 57.6%

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

   7. Applied rewrites 57.7%

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

   9. Applied rewrites 57.7%

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

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

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 71.6

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

   5. Applied rewrites 71.6%

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

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

   1. Initial program 97.2%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 88.8

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

   5. Applied rewrites 88.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 63.8%

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

4. Final simplification 68.0%

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

Alternative 6: 60.2% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 57.6

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

   5. Applied rewrites 57.6%

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

   7. Applied rewrites 57.7%

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

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

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 71.6

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

   5. Applied rewrites 71.6%

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

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

   1. Initial program 97.2%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 88.8

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

   5. Applied rewrites 88.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 63.8%

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

4. Final simplification 68.0%

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

Alternative 7: 59.4% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (60.0d0 / (z - t)) * x
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-1d+82)) then
        tmp = t_1
    else if (t_2 <= 1d+124) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+82], t$95$1, If[LessEqual[t$95$2, 1e+124], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.3%

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

   3. 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 56.9

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

   5. Applied rewrites 56.9%

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

   7. Applied rewrites 56.9%

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

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

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 71.2

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

   5. Applied rewrites 71.2%

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

4. Final simplification 66.7%

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

Alternative 8: 57.3% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+82], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+124], N[(120.0 * a), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 97.4%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 90.9

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

   5. Applied rewrites 90.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 47.7%

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

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

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 71.2

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

   5. Applied rewrites 71.2%

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

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

   1. Initial program 97.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 56.0

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

   5. Applied rewrites 56.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 43.4%

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

4. Final simplification 63.2%

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

Alternative 9: 54.2% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

   1. Initial program 97.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 58.8

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

   5. Applied rewrites 58.8%

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

   7. Applied rewrites 58.9%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 39.2%

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

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

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 70.8

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

   5. Applied rewrites 70.8%

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

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

   1. Initial program 97.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 56.0

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

   5. Applied rewrites 56.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 43.4%

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

4. Final simplification 61.6%

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

Alternative 10: 54.2% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (60.0d0 / z) * x
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-2d+88)) then
        tmp = t_1
    else if (t_2 <= 1d+124) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 / z), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+88], t$95$1, If[LessEqual[t$95$2, 1e+124], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 57.6

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

   5. Applied rewrites 57.6%

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

   7. Applied rewrites 57.6%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 41.0%

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

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

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 70.8

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

   5. Applied rewrites 70.8%

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

4. Final simplification 61.6%

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

Alternative 11: 54.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+216}:\\ \;\;\;\;\frac{y}{t} \cdot 60\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+184}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{t} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+216)
     (* (/ y t) 60.0)
     (if (<= t_1 5e+184) (* 120.0 a) (* (/ -60.0 t) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+216) {
		tmp = (y / t) * 60.0;
	} else if (t_1 <= 5e+184) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 / t) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-1d+216)) then
        tmp = (y / t) * 60.0d0
    else if (t_1 <= 5d+184) then
        tmp = 120.0d0 * a
    else
        tmp = ((-60.0d0) / t) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+216) {
		tmp = (y / t) * 60.0;
	} else if (t_1 <= 5e+184) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 / t) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+216:
		tmp = (y / t) * 60.0
	elif t_1 <= 5e+184:
		tmp = 120.0 * a
	else:
		tmp = (-60.0 / t) * x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+216)
		tmp = Float64(Float64(y / t) * 60.0);
	elseif (t_1 <= 5e+184)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(-60.0 / t) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+216)
		tmp = (y / t) * 60.0;
	elseif (t_1 <= 5e+184)
		tmp = 120.0 * a;
	else
		tmp = (-60.0 / t) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+216], N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+184], N[(120.0 * a), $MachinePrecision], N[(N[(-60.0 / t), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1e216

   1. Initial program 95.3%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 99.6

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

   5. Applied rewrites 99.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 64.2%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 38.0%

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

   if -1e216 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.9999999999999999e184

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 63.2

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

   5. Applied rewrites 63.2%

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

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

   1. Initial program 95.8%

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

   3. 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 52.4

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

   5. Applied rewrites 52.4%

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

   7. Applied rewrites 52.3%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 33.3%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+216}:\\ \;\;\;\;\frac{y}{t} \cdot 60\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+184}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{t} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+216}:\\ \;\;\;\;\frac{y}{t} \cdot 60\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+184}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+216)
     (* (/ y t) 60.0)
     (if (<= t_1 5e+184) (* 120.0 a) (* (/ x t) -60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+216) {
		tmp = (y / t) * 60.0;
	} else if (t_1 <= 5e+184) {
		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 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-1d+216)) then
        tmp = (y / t) * 60.0d0
    else if (t_1 <= 5d+184) 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 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+216) {
		tmp = (y / t) * 60.0;
	} else if (t_1 <= 5e+184) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / t) * -60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+216:
		tmp = (y / t) * 60.0
	elif t_1 <= 5e+184:
		tmp = 120.0 * a
	else:
		tmp = (x / t) * -60.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+216)
		tmp = Float64(Float64(y / t) * 60.0);
	elseif (t_1 <= 5e+184)
		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 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+216)
		tmp = (y / t) * 60.0;
	elseif (t_1 <= 5e+184)
		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[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+216], N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+184], 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)) < -1e216

   1. Initial program 95.3%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 99.6

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

   5. Applied rewrites 99.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 64.2%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 38.0%

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

   if -1e216 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.9999999999999999e184

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 63.2

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

   5. Applied rewrites 63.2%

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

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

   1. Initial program 95.8%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 95.3

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

   5. Applied rewrites 95.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 43.2%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 33.2%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+216}:\\ \;\;\;\;\frac{y}{t} \cdot 60\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+184}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t} \cdot 60\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+221}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y t) 60.0)) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -1e+216) t_1 (if (<= t_2 1e+221) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / t) * 60.0;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+216) {
		tmp = t_1;
	} else if (t_2 <= 1e+221) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y / t) * 60.0d0
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-1d+216)) then
        tmp = t_1
    else if (t_2 <= 1d+221) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / t) * 60.0;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+216) {
		tmp = t_1;
	} else if (t_2 <= 1e+221) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / t) * 60.0
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -1e+216:
		tmp = t_1
	elif t_2 <= 1e+221:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / t) * 60.0)
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+216)
		tmp = t_1;
	elseif (t_2 <= 1e+221)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / t) * 60.0;
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+216)
		tmp = t_1;
	elseif (t_2 <= 1e+221)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+216], t$95$1, If[LessEqual[t$95$2, 1e+221], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1e216 or 1e221 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 95.0%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 99.5

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

   5. Applied rewrites 99.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 55.7%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 31.9%

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

   if -1e216 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1e221

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 62.0

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

   5. Applied rewrites 62.0%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+216}:\\ \;\;\;\;\frac{y}{t} \cdot 60\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+221}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot 60\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 74.1% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 78.9

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 79.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 79.4

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

   10. Applied rewrites 79.4%

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

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

   1. Initial program 99.0%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 74.7

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

   5. Applied rewrites 74.7%

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

   7. Applied rewrites 74.1%

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

   9. Applied rewrites 74.9%

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

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

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 84.5

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

   5. Applied rewrites 84.5%

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

4. Final simplification 78.4%

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

Alternative 15: 75.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5.6 \cdot 10^{+41}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;120 \cdot a \leq 3.4 \cdot 10^{+42}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* 120.0 a) -5.6e+41)
   (* 120.0 a)
   (if (<= (* 120.0 a) 3.4e+42) (* (/ 60.0 (- z t)) (- x y)) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -5.6e+41) {
		tmp = 120.0 * a;
	} else if ((120.0 * a) <= 3.4e+42) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((120.0d0 * a) <= (-5.6d+41)) then
        tmp = 120.0d0 * a
    else if ((120.0d0 * a) <= 3.4d+42) then
        tmp = (60.0d0 / (z - t)) * (x - y)
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -5.6e+41) {
		tmp = 120.0 * a;
	} else if ((120.0 * a) <= 3.4e+42) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (120.0 * a) <= -5.6e+41:
		tmp = 120.0 * a
	elif (120.0 * a) <= 3.4e+42:
		tmp = (60.0 / (z - t)) * (x - y)
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(120.0 * a) <= -5.6e+41)
		tmp = Float64(120.0 * a);
	elseif (Float64(120.0 * a) <= 3.4e+42)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((120.0 * a) <= -5.6e+41)
		tmp = 120.0 * a;
	elseif ((120.0 * a) <= 3.4e+42)
		tmp = (60.0 / (z - t)) * (x - y);
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(120.0 * a), $MachinePrecision], -5.6e+41], N[(120.0 * a), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], 3.4e+42], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.5999999999999999e41 or 3.39999999999999975e42 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 81.2

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

   5. Applied rewrites 81.2%

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

   if -5.5999999999999999e41 < (*.f64 a #s(literal 120 binary64)) < 3.39999999999999975e42

   1. Initial program 99.0%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 74.7

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

   5. Applied rewrites 74.7%

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

   7. Applied rewrites 74.7%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5.6 \cdot 10^{+41}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;120 \cdot a \leq 3.4 \cdot 10^{+42}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 89.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{t - z}, 60, 120 \cdot a\right)\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+70}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + 120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y (- t z)) 60.0 (* 120.0 a))))
   (if (<= y -4.2e+56)
     t_1
     (if (<= y 3.8e+70) (+ (/ (* 60.0 x) (- z t)) (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / (t - z)), 60.0, (120.0 * a));
	double tmp;
	if (y <= -4.2e+56) {
		tmp = t_1;
	} else if (y <= 3.8e+70) {
		tmp = ((60.0 * x) / (z - t)) + (120.0 * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y / Float64(t - z)), 60.0, Float64(120.0 * a))
	tmp = 0.0
	if (y <= -4.2e+56)
		tmp = t_1;
	elseif (y <= 3.8e+70)
		tmp = Float64(Float64(Float64(60.0 * x) / Float64(z - t)) + 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 / N[(t - z), $MachinePrecision]), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e+56], t$95$1, If[LessEqual[y, 3.8e+70], N[(N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.20000000000000034e56 or 3.7999999999999998e70 < y

   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 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 89.9

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

   7. Applied rewrites 89.9%

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

   if -4.20000000000000034e56 < y < 3.7999999999999998e70

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 95.8

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

   5. Applied rewrites 95.8%

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

4. Final simplification 93.8%

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

Alternative 17: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 120, \frac{x - y}{-0.016666666666666666 \cdot t}\right)\\ \mathbf{if}\;t \leq -23500:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{0.016666666666666666 \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma a 120.0 (/ (- x y) (* -0.016666666666666666 t)))))
   (if (<= t -23500.0)
     t_1
     (if (<= t 2e-7)
       (fma a 120.0 (/ (- x y) (* 0.016666666666666666 z)))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(a, 120.0, ((x - y) / (-0.016666666666666666 * t)));
	double tmp;
	if (t <= -23500.0) {
		tmp = t_1;
	} else if (t <= 2e-7) {
		tmp = fma(a, 120.0, ((x - y) / (0.016666666666666666 * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(a, 120.0, Float64(Float64(x - y) / Float64(-0.016666666666666666 * t)))
	tmp = 0.0
	if (t <= -23500.0)
		tmp = t_1;
	elseif (t <= 2e-7)
		tmp = fma(a, 120.0, Float64(Float64(x - y) / Float64(0.016666666666666666 * z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a * 120.0 + N[(N[(x - y), $MachinePrecision] / N[(-0.016666666666666666 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -23500.0], t$95$1, If[LessEqual[t, 2e-7], N[(a * 120.0 + N[(N[(x - y), $MachinePrecision] / N[(0.016666666666666666 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -23500 or 1.9999999999999999e-7 < t

   1. Initial program 99.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.1

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. div-inv N/A

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

      8. lower-*.f64 N/A

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

      9. metadata-eval 99.9

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

   6. Applied rewrites 99.9%

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

   7. Taylor expanded in t around inf

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

      1. lower-*.f64 93.2

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

   9. Applied rewrites 93.2%

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

   if -23500 < t < 1.9999999999999999e-7

   1. Initial program 99.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.1

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. div-inv N/A

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

      8. lower-*.f64 N/A

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

      9. metadata-eval 99.9

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

   6. Applied rewrites 99.9%

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

   7. Taylor expanded in t around 0

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

      1. lower-*.f64 85.8

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

   9. Applied rewrites 85.8%

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{x - y}{\color{blue}{0.016666666666666666 \cdot z}}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 120, \frac{x - y}{-0.016666666666666666 \cdot t}\right)\\ \mathbf{if}\;t \leq -23500:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma a 120.0 (/ (- x y) (* -0.016666666666666666 t)))))
   (if (<= t -23500.0)
     t_1
     (if (<= t 2e-7) (fma (/ (- x y) z) 60.0 (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(a, 120.0, ((x - y) / (-0.016666666666666666 * t)));
	double tmp;
	if (t <= -23500.0) {
		tmp = t_1;
	} else if (t <= 2e-7) {
		tmp = fma(((x - y) / z), 60.0, (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(a, 120.0, Float64(Float64(x - y) / Float64(-0.016666666666666666 * t)))
	tmp = 0.0
	if (t <= -23500.0)
		tmp = t_1;
	elseif (t <= 2e-7)
		tmp = fma(Float64(Float64(x - y) / z), 60.0, Float64(120.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a * 120.0 + N[(N[(x - y), $MachinePrecision] / N[(-0.016666666666666666 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -23500.0], t$95$1, If[LessEqual[t, 2e-7], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -23500 or 1.9999999999999999e-7 < t

   1. Initial program 99.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.1

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. div-inv N/A

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

      8. lower-*.f64 N/A

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

      9. metadata-eval 99.9

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

   6. Applied rewrites 99.9%

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

   7. Taylor expanded in t around inf

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

      1. lower-*.f64 93.2

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

   9. Applied rewrites 93.2%

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

   if -23500 < t < 1.9999999999999999e-7

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 85.6

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

   5. Applied rewrites 85.6%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -23500:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{-0.016666666666666666 \cdot t}\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{-0.016666666666666666 \cdot t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 85.0% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if t < -23500

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.9

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

      5. lift-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. frac-2neg N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. neg-sub0 N/A

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

      15. lift--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 93.5

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

   7. Applied rewrites 93.5%

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

   if -23500 < t < 1.9999999999999999e-7

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 85.6

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

   5. Applied rewrites 85.6%

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

   if 1.9999999999999999e-7 < t

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 92.8

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

   5. Applied rewrites 92.8%

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

4. Final simplification 89.5%

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

Alternative 20: 85.0% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if t < -23500 or 1.9999999999999999e-7 < t

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 93.1

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

   5. Applied rewrites 93.1%

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

   if -23500 < t < 1.9999999999999999e-7

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 85.6

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

   5. Applied rewrites 85.6%

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

4. Final simplification 89.5%

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

Alternative 21: 99.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 99.1

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

   5. lift-/.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. *-commutative N/A

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

   8. associate-/l* N/A

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

   9. *-commutative N/A

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

   10. lower-*.f64 N/A

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

   11. frac-2neg N/A

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

   12. lower-/.f64 N/A

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

   13. metadata-eval N/A

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

   14. neg-sub0 N/A

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

   15. lift--.f64 N/A

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

   16. sub-neg N/A

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

   17. +-commutative N/A

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

   18. associate--r+ N/A

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

   19. neg-sub0 N/A

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

   20. remove-double-neg N/A

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

   21. lower--.f64 99.8

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

4. Applied rewrites 99.8%

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

Alternative 22: 50.6% accurate, 5.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

3. Taylor expanded in z around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 52.6

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

5. Applied rewrites 52.6%

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

6. Final simplification 52.6%

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

Developer Target 1: 99.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024235 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (/ 60 (/ (- z t) (- x y))) (* a 120)))

  (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))