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

Percentage Accurate: 99.4% → 99.4%

Time: 10.0s

Alternatives: 17

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 2: 73.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot 60}{t - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+70}:\\ \;\;\;\;\frac{y - x}{-0.016666666666666666 \cdot \left(z - t\right)}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-131}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y \cdot 60}{t}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-47}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{t} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y x) 60.0) (- t z))))
   (if (<= t_1 -1e+70)
     (/ (- y x) (* -0.016666666666666666 (- z t)))
     (if (<= t_1 -5e-131)
       (fma a 120.0 (/ (* y 60.0) t))
       (if (<= t_1 5e-47)
         (* 120.0 a)
         (if (<= t_1 5e+72) (fma a 120.0 (* (/ x t) -60.0)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - x) * 60.0) / (t - z);
	double tmp;
	if (t_1 <= -1e+70) {
		tmp = (y - x) / (-0.016666666666666666 * (z - t));
	} else if (t_1 <= -5e-131) {
		tmp = fma(a, 120.0, ((y * 60.0) / t));
	} else if (t_1 <= 5e-47) {
		tmp = 120.0 * a;
	} else if (t_1 <= 5e+72) {
		tmp = fma(a, 120.0, ((x / t) * -60.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - x) * 60.0) / Float64(t - z))
	tmp = 0.0
	if (t_1 <= -1e+70)
		tmp = Float64(Float64(y - x) / Float64(-0.016666666666666666 * Float64(z - t)));
	elseif (t_1 <= -5e-131)
		tmp = fma(a, 120.0, Float64(Float64(y * 60.0) / t));
	elseif (t_1 <= 5e-47)
		tmp = Float64(120.0 * a);
	elseif (t_1 <= 5e+72)
		tmp = fma(a, 120.0, Float64(Float64(x / t) * -60.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - x), $MachinePrecision] * 60.0), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+70], N[(N[(y - x), $MachinePrecision] / N[(-0.016666666666666666 * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-131], N[(a * 120.0 + N[(N[(y * 60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-47], N[(120.0 * a), $MachinePrecision], If[LessEqual[t$95$1, 5e+72], N[(a * 120.0 + N[(N[(x / t), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.00000000000000007e70

   1. Initial program 99.7%

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

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

      3. lift-*.f64 N/A

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

      4. associate-/r* N/A

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

      5. clear-num-rev N/A

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

      6. lower-/.f64 N/A

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

      7. div-inv N/A

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

      8. metadata-eval N/A

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. metadata-eval 99.7

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

   4. Applied rewrites 99.7%

      \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 99.8

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. associate-*r/ N/A

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

      4. div-add-rev N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. cancel-sign-sub-inv N/A

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

      10. metadata-eval N/A

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

      11. distribute-lft-out-- N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 83.7

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

   9. Applied rewrites 83.7%

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

   if -1.00000000000000007e70 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.0000000000000004e-131

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 72.8

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

   5. Applied rewrites 72.8%

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

   7. Applied rewrites 72.9%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 82.2%

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

       1. lift-+.f64 N/A

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

       2. +-commutative N/A

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

       3. lift-*.f64 N/A

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

       4. lower-fma.f64 82.2

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

   12. Applied rewrites 82.2%

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

   if -5.0000000000000004e-131 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.00000000000000011e-47

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 88.2

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

   5. Applied rewrites 88.2%

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

   if 5.00000000000000011e-47 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999992e72

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 73.2

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

   5. Applied rewrites 73.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 76.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 76.7

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

   10. Applied rewrites 76.7%

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

   if 4.99999999999999992e72 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 10.3

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

   5. Applied rewrites 10.3%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 92.1

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

   8. Applied rewrites 92.1%

      \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot 60}{z - t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq -1 \cdot 10^{+70}:\\ \;\;\;\;\frac{y - x}{-0.016666666666666666 \cdot \left(z - t\right)}\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq -5 \cdot 10^{-131}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y \cdot 60}{t}\right)\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq 5 \cdot 10^{-47}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq 5 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{t} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot 60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot 60}{t - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+70}:\\ \;\;\;\;\frac{y - x}{-0.016666666666666666 \cdot \left(z - t\right)}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-131}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-47}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{t} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y x) 60.0) (- t z))))
   (if (<= t_1 -1e+70)
     (/ (- y x) (* -0.016666666666666666 (- z t)))
     (if (<= t_1 -5e-131)
       (fma (/ y t) 60.0 (* 120.0 a))
       (if (<= t_1 5e-47)
         (* 120.0 a)
         (if (<= t_1 5e+72) (fma a 120.0 (* (/ x t) -60.0)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - x) * 60.0) / (t - z);
	double tmp;
	if (t_1 <= -1e+70) {
		tmp = (y - x) / (-0.016666666666666666 * (z - t));
	} else if (t_1 <= -5e-131) {
		tmp = fma((y / t), 60.0, (120.0 * a));
	} else if (t_1 <= 5e-47) {
		tmp = 120.0 * a;
	} else if (t_1 <= 5e+72) {
		tmp = fma(a, 120.0, ((x / t) * -60.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - x) * 60.0) / Float64(t - z))
	tmp = 0.0
	if (t_1 <= -1e+70)
		tmp = Float64(Float64(y - x) / Float64(-0.016666666666666666 * Float64(z - t)));
	elseif (t_1 <= -5e-131)
		tmp = fma(Float64(y / t), 60.0, Float64(120.0 * a));
	elseif (t_1 <= 5e-47)
		tmp = Float64(120.0 * a);
	elseif (t_1 <= 5e+72)
		tmp = fma(a, 120.0, Float64(Float64(x / t) * -60.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - x), $MachinePrecision] * 60.0), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+70], N[(N[(y - x), $MachinePrecision] / N[(-0.016666666666666666 * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-131], N[(N[(y / t), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-47], N[(120.0 * a), $MachinePrecision], If[LessEqual[t$95$1, 5e+72], N[(a * 120.0 + N[(N[(x / t), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.00000000000000007e70

   1. Initial program 99.7%

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

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

      3. lift-*.f64 N/A

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

      4. associate-/r* N/A

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

      5. clear-num-rev N/A

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

      6. lower-/.f64 N/A

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

      7. div-inv N/A

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

      8. metadata-eval N/A

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. metadata-eval 99.7

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

   4. Applied rewrites 99.7%

      \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 99.8

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. associate-*r/ N/A

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

      4. div-add-rev N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. cancel-sign-sub-inv N/A

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

      10. metadata-eval N/A

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

      11. distribute-lft-out-- N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 83.7

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

   9. Applied rewrites 83.7%

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

   if -1.00000000000000007e70 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.0000000000000004e-131

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 86.6

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

   5. Applied rewrites 86.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 82.2%

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

   if -5.0000000000000004e-131 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.00000000000000011e-47

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 88.2

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

   5. Applied rewrites 88.2%

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

   if 5.00000000000000011e-47 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999992e72

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 73.2

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

   5. Applied rewrites 73.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 76.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 76.7

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

   10. Applied rewrites 76.7%

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

   if 4.99999999999999992e72 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 10.3

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

   5. Applied rewrites 10.3%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 92.1

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

   8. Applied rewrites 92.1%

      \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot 60}{z - t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq -1 \cdot 10^{+70}:\\ \;\;\;\;\frac{y - x}{-0.016666666666666666 \cdot \left(z - t\right)}\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq -5 \cdot 10^{-131}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq 5 \cdot 10^{-47}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq 5 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{t} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot 60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot 60}{t - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+70}:\\ \;\;\;\;\frac{y - x}{-0.016666666666666666 \cdot \left(z - t\right)}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-131}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+52}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y x) 60.0) (- t z))))
   (if (<= t_1 -1e+70)
     (/ (- y x) (* -0.016666666666666666 (- z t)))
     (if (<= t_1 -5e-131)
       (fma (/ y t) 60.0 (* 120.0 a))
       (if (<= t_1 2e+52) (* 120.0 a) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - x) * 60.0) / (t - z);
	double tmp;
	if (t_1 <= -1e+70) {
		tmp = (y - x) / (-0.016666666666666666 * (z - t));
	} else if (t_1 <= -5e-131) {
		tmp = fma((y / t), 60.0, (120.0 * a));
	} else if (t_1 <= 2e+52) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - x) * 60.0) / Float64(t - z))
	tmp = 0.0
	if (t_1 <= -1e+70)
		tmp = Float64(Float64(y - x) / Float64(-0.016666666666666666 * Float64(z - t)));
	elseif (t_1 <= -5e-131)
		tmp = fma(Float64(y / t), 60.0, Float64(120.0 * a));
	elseif (t_1 <= 2e+52)
		tmp = 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[(y - x), $MachinePrecision] * 60.0), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+70], N[(N[(y - x), $MachinePrecision] / N[(-0.016666666666666666 * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-131], N[(N[(y / t), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+52], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.00000000000000007e70

   1. Initial program 99.7%

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

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

      3. lift-*.f64 N/A

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

      4. associate-/r* N/A

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

      5. clear-num-rev N/A

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

      6. lower-/.f64 N/A

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

      7. div-inv N/A

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

      8. metadata-eval N/A

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. metadata-eval 99.7

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

   4. Applied rewrites 99.7%

      \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 99.8

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. associate-*r/ N/A

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

      4. div-add-rev N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. cancel-sign-sub-inv N/A

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

      10. metadata-eval N/A

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

      11. distribute-lft-out-- N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 83.7

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

   9. Applied rewrites 83.7%

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

   if -1.00000000000000007e70 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.0000000000000004e-131

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 86.6

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

   5. Applied rewrites 86.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 82.2%

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

   if -5.0000000000000004e-131 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e52

   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. lower-*.f64 81.0

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

   5. Applied rewrites 81.0%

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

   if 2e52 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 12.3

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

   5. Applied rewrites 12.3%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 90.2

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

   8. Applied rewrites 90.2%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq -1 \cdot 10^{+70}:\\ \;\;\;\;\frac{y - x}{-0.016666666666666666 \cdot \left(z - t\right)}\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq -5 \cdot 10^{-131}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq 2 \cdot 10^{+52}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot 60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot 60}{t - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-131}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+52}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y x) 60.0) (- t z))))
   (if (<= t_1 -1e+70)
     t_1
     (if (<= t_1 -5e-131)
       (fma (/ y t) 60.0 (* 120.0 a))
       (if (<= t_1 2e+52) (* 120.0 a) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - x) * 60.0) / (t - z);
	double tmp;
	if (t_1 <= -1e+70) {
		tmp = t_1;
	} else if (t_1 <= -5e-131) {
		tmp = fma((y / t), 60.0, (120.0 * a));
	} else if (t_1 <= 2e+52) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - x) * 60.0) / Float64(t - z))
	tmp = 0.0
	if (t_1 <= -1e+70)
		tmp = t_1;
	elseif (t_1 <= -5e-131)
		tmp = fma(Float64(y / t), 60.0, Float64(120.0 * a));
	elseif (t_1 <= 2e+52)
		tmp = 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[(y - x), $MachinePrecision] * 60.0), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+70], t$95$1, If[LessEqual[t$95$1, -5e-131], N[(N[(y / t), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+52], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.00000000000000007e70 or 2e52 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 15.3

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

   5. Applied rewrites 15.3%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 86.2

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

   8. Applied rewrites 86.2%

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

   if -1.00000000000000007e70 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.0000000000000004e-131

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 86.6

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

   5. Applied rewrites 86.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 82.2%

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

   if -5.0000000000000004e-131 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e52

   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. lower-*.f64 81.0

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

   5. Applied rewrites 81.0%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq -1 \cdot 10^{+70}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot 60}{t - z}\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq -5 \cdot 10^{-131}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq 2 \cdot 10^{+52}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot 60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{60}{t - z}\\ t_2 := \frac{\left(y - x\right) \cdot 60}{t - z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-131}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+52}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ 60.0 (- t z)))) (t_2 (/ (* (- y x) 60.0) (- t z))))
   (if (<= t_2 -1e+70)
     t_1
     (if (<= t_2 -5e-131)
       (fma (/ y t) 60.0 (* 120.0 a))
       (if (<= t_2 2e+52) (* 120.0 a) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - x) * (60.0 / (t - z));
	double t_2 = ((y - x) * 60.0) / (t - z);
	double tmp;
	if (t_2 <= -1e+70) {
		tmp = t_1;
	} else if (t_2 <= -5e-131) {
		tmp = fma((y / t), 60.0, (120.0 * a));
	} else if (t_2 <= 2e+52) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - x) * Float64(60.0 / Float64(t - z)))
	t_2 = Float64(Float64(Float64(y - x) * 60.0) / Float64(t - z))
	tmp = 0.0
	if (t_2 <= -1e+70)
		tmp = t_1;
	elseif (t_2 <= -5e-131)
		tmp = fma(Float64(y / t), 60.0, Float64(120.0 * a));
	elseif (t_2 <= 2e+52)
		tmp = 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 - x), $MachinePrecision] * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y - x), $MachinePrecision] * 60.0), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+70], t$95$1, If[LessEqual[t$95$2, -5e-131], N[(N[(y / t), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+52], N[(120.0 * a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.00000000000000007e70 or 2e52 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 86.2

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

   5. Applied rewrites 86.2%

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

   if -1.00000000000000007e70 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.0000000000000004e-131

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 86.6

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

   5. Applied rewrites 86.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 82.2%

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

   if -5.0000000000000004e-131 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e52

   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. lower-*.f64 81.0

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

   5. Applied rewrites 81.0%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq -1 \cdot 10^{+70}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{60}{t - z}\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq -5 \cdot 10^{-131}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq 2 \cdot 10^{+52}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot 60}{t - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+70}:\\ \;\;\;\;\frac{y - x}{-0.016666666666666666 \cdot \left(z - t\right)}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(120, a, \frac{y}{z - t} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y x) 60.0) (- t z))))
   (if (<= t_1 -1e+70)
     (/ (- y x) (* -0.016666666666666666 (- z t)))
     (if (<= t_1 5e+72) (fma 120.0 a (* (/ y (- z t)) -60.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - x) * 60.0) / (t - z);
	double tmp;
	if (t_1 <= -1e+70) {
		tmp = (y - x) / (-0.016666666666666666 * (z - t));
	} else if (t_1 <= 5e+72) {
		tmp = fma(120.0, a, ((y / (z - t)) * -60.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - x) * 60.0) / Float64(t - z))
	tmp = 0.0
	if (t_1 <= -1e+70)
		tmp = Float64(Float64(y - x) / Float64(-0.016666666666666666 * Float64(z - t)));
	elseif (t_1 <= 5e+72)
		tmp = fma(120.0, a, Float64(Float64(y / Float64(z - t)) * -60.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - x), $MachinePrecision] * 60.0), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+70], N[(N[(y - x), $MachinePrecision] / N[(-0.016666666666666666 * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+72], N[(120.0 * a + N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.00000000000000007e70

   1. Initial program 99.7%

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

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

      3. lift-*.f64 N/A

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

      4. associate-/r* N/A

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

      5. clear-num-rev N/A

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

      6. lower-/.f64 N/A

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

      7. div-inv N/A

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

      8. metadata-eval N/A

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. metadata-eval 99.7

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

   4. Applied rewrites 99.7%

      \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 99.8

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. associate-*r/ N/A

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

      4. div-add-rev N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. cancel-sign-sub-inv N/A

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

      10. metadata-eval N/A

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

      11. distribute-lft-out-- N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 83.7

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

   9. Applied rewrites 83.7%

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

   if -1.00000000000000007e70 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999992e72

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 88.0

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

   5. Applied rewrites 88.0%

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

   if 4.99999999999999992e72 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 10.3

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

   5. Applied rewrites 10.3%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 92.1

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

   8. Applied rewrites 92.1%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq -1 \cdot 10^{+70}:\\ \;\;\;\;\frac{y - x}{-0.016666666666666666 \cdot \left(z - t\right)}\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq 5 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(120, a, \frac{y}{z - t} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot 60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot 60}{t - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+70}:\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+72}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y x) 60.0) (- t z))))
   (if (<= t_1 -1e+70)
     (* (/ x (- z t)) 60.0)
     (if (<= t_1 5e+72) (* 120.0 a) (* (/ y (- z t)) -60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - x) * 60.0) / (t - z);
	double tmp;
	if (t_1 <= -1e+70) {
		tmp = (x / (z - t)) * 60.0;
	} else if (t_1 <= 5e+72) {
		tmp = 120.0 * a;
	} else {
		tmp = (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 = ((y - x) * 60.0d0) / (t - z)
    if (t_1 <= (-1d+70)) then
        tmp = (x / (z - t)) * 60.0d0
    else if (t_1 <= 5d+72) then
        tmp = 120.0d0 * a
    else
        tmp = (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 = ((y - x) * 60.0) / (t - z);
	double tmp;
	if (t_1 <= -1e+70) {
		tmp = (x / (z - t)) * 60.0;
	} else if (t_1 <= 5e+72) {
		tmp = 120.0 * a;
	} else {
		tmp = (y / (z - t)) * -60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - x) * 60.0) / (t - z)
	tmp = 0
	if t_1 <= -1e+70:
		tmp = (x / (z - t)) * 60.0
	elif t_1 <= 5e+72:
		tmp = 120.0 * a
	else:
		tmp = (y / (z - t)) * -60.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - x) * 60.0) / Float64(t - z))
	tmp = 0.0
	if (t_1 <= -1e+70)
		tmp = Float64(Float64(x / Float64(z - t)) * 60.0);
	elseif (t_1 <= 5e+72)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(y / Float64(z - t)) * -60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - x) * 60.0) / (t - z);
	tmp = 0.0;
	if (t_1 <= -1e+70)
		tmp = (x / (z - t)) * 60.0;
	elseif (t_1 <= 5e+72)
		tmp = 120.0 * a;
	else
		tmp = (y / (z - t)) * -60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - x), $MachinePrecision] * 60.0), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+70], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+72], N[(120.0 * a), $MachinePrecision], N[(N[(y / 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)) < -1.00000000000000007e70

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 49.1

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

   5. Applied rewrites 49.1%

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

   if -1.00000000000000007e70 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999992e72

   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. lower-*.f64 77.0

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

   5. Applied rewrites 77.0%

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

   if 4.99999999999999992e72 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 10.3

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

   5. Applied rewrites 10.3%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 92.1

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

   8. Applied rewrites 92.1%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 46.9%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq -1 \cdot 10^{+70}:\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq 5 \cdot 10^{+72}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot 60}{t - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+70}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+72}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y x) 60.0) (- t z))))
   (if (<= t_1 -1e+70)
     (* (/ 60.0 (- z t)) x)
     (if (<= t_1 5e+72) (* 120.0 a) (* (/ y (- z t)) -60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - x) * 60.0) / (t - z);
	double tmp;
	if (t_1 <= -1e+70) {
		tmp = (60.0 / (z - t)) * x;
	} else if (t_1 <= 5e+72) {
		tmp = 120.0 * a;
	} else {
		tmp = (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 = ((y - x) * 60.0d0) / (t - z)
    if (t_1 <= (-1d+70)) then
        tmp = (60.0d0 / (z - t)) * x
    else if (t_1 <= 5d+72) then
        tmp = 120.0d0 * a
    else
        tmp = (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 = ((y - x) * 60.0) / (t - z);
	double tmp;
	if (t_1 <= -1e+70) {
		tmp = (60.0 / (z - t)) * x;
	} else if (t_1 <= 5e+72) {
		tmp = 120.0 * a;
	} else {
		tmp = (y / (z - t)) * -60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - x) * 60.0) / (t - z)
	tmp = 0
	if t_1 <= -1e+70:
		tmp = (60.0 / (z - t)) * x
	elif t_1 <= 5e+72:
		tmp = 120.0 * a
	else:
		tmp = (y / (z - t)) * -60.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - x) * 60.0) / Float64(t - z))
	tmp = 0.0
	if (t_1 <= -1e+70)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * x);
	elseif (t_1 <= 5e+72)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(y / Float64(z - t)) * -60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - x) * 60.0) / (t - z);
	tmp = 0.0;
	if (t_1 <= -1e+70)
		tmp = (60.0 / (z - t)) * x;
	elseif (t_1 <= 5e+72)
		tmp = 120.0 * a;
	else
		tmp = (y / (z - t)) * -60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - x), $MachinePrecision] * 60.0), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+70], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 5e+72], N[(120.0 * a), $MachinePrecision], N[(N[(y / 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)) < -1.00000000000000007e70

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 49.1

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

   5. Applied rewrites 49.1%

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

   7. Applied rewrites 49.0%

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

   if -1.00000000000000007e70 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999992e72

   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. lower-*.f64 77.0

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

   5. Applied rewrites 77.0%

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

   if 4.99999999999999992e72 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 10.3

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

   5. Applied rewrites 10.3%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 92.1

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

   8. Applied rewrites 92.1%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 46.9%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq -1 \cdot 10^{+70}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq 5 \cdot 10^{+72}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z - t} \cdot -60\\ t_2 := \frac{\left(y - x\right) \cdot 60}{t - z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+72}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y (- z t)) -60.0)) (t_2 (/ (* (- y x) 60.0) (- t z))))
   (if (<= t_2 -1e+108) t_1 (if (<= t_2 5e+72) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (z - t)) * -60.0;
	double t_2 = ((y - x) * 60.0) / (t - z);
	double tmp;
	if (t_2 <= -1e+108) {
		tmp = t_1;
	} else if (t_2 <= 5e+72) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y / (z - t)) * (-60.0d0)
    t_2 = ((y - x) * 60.0d0) / (t - z)
    if (t_2 <= (-1d+108)) then
        tmp = t_1
    else if (t_2 <= 5d+72) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (z - t)) * -60.0;
	double t_2 = ((y - x) * 60.0) / (t - z);
	double tmp;
	if (t_2 <= -1e+108) {
		tmp = t_1;
	} else if (t_2 <= 5e+72) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / (z - t)) * -60.0
	t_2 = ((y - x) * 60.0) / (t - z)
	tmp = 0
	if t_2 <= -1e+108:
		tmp = t_1
	elif t_2 <= 5e+72:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / Float64(z - t)) * -60.0)
	t_2 = Float64(Float64(Float64(y - x) * 60.0) / Float64(t - z))
	tmp = 0.0
	if (t_2 <= -1e+108)
		tmp = t_1;
	elseif (t_2 <= 5e+72)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / (z - t)) * -60.0;
	t_2 = ((y - x) * 60.0) / (t - z);
	tmp = 0.0;
	if (t_2 <= -1e+108)
		tmp = t_1;
	elseif (t_2 <= 5e+72)
		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 / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y - x), $MachinePrecision] * 60.0), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+108], t$95$1, If[LessEqual[t$95$2, 5e+72], 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)) < -1e108 or 4.99999999999999992e72 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 11.9

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

   5. Applied rewrites 11.9%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 89.5

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

   8. Applied rewrites 89.5%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 45.6%

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

   if -1e108 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999992e72

   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. lower-*.f64 74.4

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

   5. Applied rewrites 74.4%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq -1 \cdot 10^{+108}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq 5 \cdot 10^{+72}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot 60}{t - z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+189}:\\ \;\;\;\;\frac{-60 \cdot y}{-t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+72}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-t} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y x) 60.0) (- t z))))
   (if (<= t_1 -4e+189)
     (/ (* -60.0 y) (- t))
     (if (<= t_1 5e+72) (* 120.0 a) (* (/ x (- t)) 60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - x) * 60.0) / (t - z);
	double tmp;
	if (t_1 <= -4e+189) {
		tmp = (-60.0 * y) / -t;
	} else if (t_1 <= 5e+72) {
		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 = ((y - x) * 60.0d0) / (t - z)
    if (t_1 <= (-4d+189)) then
        tmp = ((-60.0d0) * y) / -t
    else if (t_1 <= 5d+72) 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 = ((y - x) * 60.0) / (t - z);
	double tmp;
	if (t_1 <= -4e+189) {
		tmp = (-60.0 * y) / -t;
	} else if (t_1 <= 5e+72) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / -t) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - x) * 60.0) / (t - z)
	tmp = 0
	if t_1 <= -4e+189:
		tmp = (-60.0 * y) / -t
	elif t_1 <= 5e+72:
		tmp = 120.0 * a
	else:
		tmp = (x / -t) * 60.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - x) * 60.0) / Float64(t - z))
	tmp = 0.0
	if (t_1 <= -4e+189)
		tmp = Float64(Float64(-60.0 * y) / Float64(-t));
	elseif (t_1 <= 5e+72)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x / Float64(-t)) * 60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - x) * 60.0) / (t - z);
	tmp = 0.0;
	if (t_1 <= -4e+189)
		tmp = (-60.0 * y) / -t;
	elseif (t_1 <= 5e+72)
		tmp = 120.0 * a;
	else
		tmp = (x / -t) * 60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - x), $MachinePrecision] * 60.0), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+189], N[(N[(-60.0 * y), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[t$95$1, 5e+72], 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)) < -4.0000000000000001e189

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 4.6

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

   5. Applied rewrites 4.6%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 96.6

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

   8. Applied rewrites 96.6%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 49.5%

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

   12. Taylor expanded in z around 0

       \[\leadsto \frac{-60 \cdot y}{-1 \cdot \color{blue}{t}} \]
   13. Step-by-step derivation

   14. Applied rewrites 38.7%

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

   if -4.0000000000000001e189 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999992e72

   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. lower-*.f64 69.3

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

   5. Applied rewrites 69.3%

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

   if 4.99999999999999992e72 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 45.9

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

   5. Applied rewrites 45.9%

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

   6. Taylor expanded in z around 0

      \[\leadsto \frac{x}{-1 \cdot t} \cdot 60 \]
   7. Step-by-step derivation

   8. Applied rewrites 44.0%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq -4 \cdot 10^{+189}:\\ \;\;\;\;\frac{-60 \cdot y}{-t}\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq 5 \cdot 10^{+72}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-t} \cdot 60\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{-t} \cdot 60\\ t_2 := \frac{\left(y - x\right) \cdot 60}{t - z}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+72}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ x (- t)) 60.0)) (t_2 (/ (* (- y x) 60.0) (- t z))))
   (if (<= t_2 -2e+173) t_1 (if (<= t_2 5e+72) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / -t) * 60.0;
	double t_2 = ((y - x) * 60.0) / (t - z);
	double tmp;
	if (t_2 <= -2e+173) {
		tmp = t_1;
	} else if (t_2 <= 5e+72) {
		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 / -t) * 60.0d0
    t_2 = ((y - x) * 60.0d0) / (t - z)
    if (t_2 <= (-2d+173)) then
        tmp = t_1
    else if (t_2 <= 5d+72) 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 / -t) * 60.0;
	double t_2 = ((y - x) * 60.0) / (t - z);
	double tmp;
	if (t_2 <= -2e+173) {
		tmp = t_1;
	} else if (t_2 <= 5e+72) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x / -t) * 60.0
	t_2 = ((y - x) * 60.0) / (t - z)
	tmp = 0
	if t_2 <= -2e+173:
		tmp = t_1
	elif t_2 <= 5e+72:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x / Float64(-t)) * 60.0)
	t_2 = Float64(Float64(Float64(y - x) * 60.0) / Float64(t - z))
	tmp = 0.0
	if (t_2 <= -2e+173)
		tmp = t_1;
	elseif (t_2 <= 5e+72)
		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 / -t) * 60.0;
	t_2 = ((y - x) * 60.0) / (t - z);
	tmp = 0.0;
	if (t_2 <= -2e+173)
		tmp = t_1;
	elseif (t_2 <= 5e+72)
		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 / (-t)), $MachinePrecision] * 60.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y - x), $MachinePrecision] * 60.0), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+173], t$95$1, If[LessEqual[t$95$2, 5e+72], 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)) < -2e173 or 4.99999999999999992e72 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 49.9

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

   5. Applied rewrites 49.9%

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

   6. Taylor expanded in z around 0

      \[\leadsto \frac{x}{-1 \cdot t} \cdot 60 \]
   7. Step-by-step derivation

   8. Applied rewrites 38.7%

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

   if -2e173 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999992e72

   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. lower-*.f64 71.0

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

   5. Applied rewrites 71.0%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq -2 \cdot 10^{+173}:\\ \;\;\;\;\frac{x}{-t} \cdot 60\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq 5 \cdot 10^{+72}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-t} \cdot 60\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq -5 \cdot 10^{+165}:\\ \;\;\;\;\frac{x}{z} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (/ (* (- y x) 60.0) (- t z)) -5e+165) (* (/ x z) 60.0) (* 120.0 a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((((y - x) * 60.0) / (t - z)) <= -5e+165) {
		tmp = (x / z) * 60.0;
	} 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 ((((y - x) * 60.0d0) / (t - z)) <= (-5d+165)) then
        tmp = (x / z) * 60.0d0
    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 ((((y - x) * 60.0) / (t - z)) <= -5e+165) {
		tmp = (x / z) * 60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (((y - x) * 60.0) / (t - z)) <= -5e+165:
		tmp = (x / z) * 60.0
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(Float64(y - x) * 60.0) / Float64(t - z)) <= -5e+165)
		tmp = Float64(Float64(x / z) * 60.0);
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((((y - x) * 60.0) / (t - z)) <= -5e+165)
		tmp = (x / z) * 60.0;
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(N[(y - x), $MachinePrecision] * 60.0), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], -5e+165], N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.9999999999999997e165

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 53.6

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

   5. Applied rewrites 53.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 34.2%

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

   if -4.9999999999999997e165 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 60.4

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

   5. Applied rewrites 60.4%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - x\right) \cdot 60}{t - z} \leq -5 \cdot 10^{+165}:\\ \;\;\;\;\frac{x}{z} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 88.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(120, a, \frac{y}{z - t} \cdot -60\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+63}:\\ \;\;\;\;\frac{x \cdot 60}{z - t} + 120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma 120.0 a (* (/ y (- z t)) -60.0))))
   (if (<= y -2.4e+179)
     t_1
     (if (<= y 1.1e+63) (+ (/ (* x 60.0) (- z t)) (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(120.0, a, ((y / (z - t)) * -60.0));
	double tmp;
	if (y <= -2.4e+179) {
		tmp = t_1;
	} else if (y <= 1.1e+63) {
		tmp = ((x * 60.0) / (z - t)) + (120.0 * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(120.0, a, Float64(Float64(y / Float64(z - t)) * -60.0))
	tmp = 0.0
	if (y <= -2.4e+179)
		tmp = t_1;
	elseif (y <= 1.1e+63)
		tmp = Float64(Float64(Float64(x * 60.0) / 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[(120.0 * a + N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e+179], t$95$1, If[LessEqual[y, 1.1e+63], N[(N[(N[(x * 60.0), $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 < -2.40000000000000013e179 or 1.0999999999999999e63 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 90.2

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

   5. Applied rewrites 90.2%

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

   if -2.40000000000000013e179 < y < 1.0999999999999999e63

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 92.4

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

   5. Applied rewrites 92.4%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+179}:\\ \;\;\;\;\mathsf{fma}\left(120, a, \frac{y}{z - t} \cdot -60\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+63}:\\ \;\;\;\;\frac{x \cdot 60}{z - t} + 120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(120, a, \frac{y}{z - t} \cdot -60\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+210}:\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+207}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2e+210)
   (* (/ x (- z t)) 60.0)
   (if (<= x 3.8e+207) (fma (/ y t) 60.0 (* 120.0 a)) (* (/ 60.0 (- z t)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2e+210) {
		tmp = (x / (z - t)) * 60.0;
	} else if (x <= 3.8e+207) {
		tmp = fma((y / t), 60.0, (120.0 * a));
	} else {
		tmp = (60.0 / (z - t)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2e+210)
		tmp = Float64(Float64(x / Float64(z - t)) * 60.0);
	elseif (x <= 3.8e+207)
		tmp = fma(Float64(y / t), 60.0, Float64(120.0 * a));
	else
		tmp = Float64(Float64(60.0 / Float64(z - t)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2e+210], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[x, 3.8e+207], N[(N[(y / t), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.99999999999999985e210

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-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 84.1

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

   5. Applied rewrites 84.1%

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

   if -1.99999999999999985e210 < x < 3.79999999999999986e207

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 84.8

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

   5. Applied rewrites 84.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 66.0%

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

   if 3.79999999999999986e207 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. *-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 65.8

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

   5. Applied rewrites 65.8%

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

   7. Applied rewrites 65.8%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+210}:\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+207}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 99.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. 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 99.8

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

   5. lift-/.f64 N/A

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

   6. clear-num N/A

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

   7. lift-*.f64 N/A

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

   8. associate-/r* N/A

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

   9. associate-/r/ N/A

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

   10. clear-num N/A

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

   11. lower-*.f64 N/A

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

   12. frac-2neg N/A

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

   13. lower-/.f64 N/A

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

   14. metadata-eval N/A

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

   15. neg-sub0 N/A

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

   16. lift--.f64 N/A

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

   17. sub-neg N/A

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

   18. +-commutative N/A

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

   19. associate--r+ N/A

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

   20. neg-sub0 N/A

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

   21. remove-double-neg N/A

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

   22. 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. Final simplification 99.8%

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

Alternative 17: 50.3% 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 99.8%

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

3. Taylor expanded in z around inf

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

   1. lower-*.f64 52.2

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

5. Applied rewrites 52.2%

   \[\leadsto \color{blue}{120 \cdot a} \]
6. 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 2024298 
(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)))