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

Percentage Accurate: 99.3% → 99.8%

Time: 12.6s

Alternatives: 15

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

   1. lift--.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. remove-double-neg N/A

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

   4. lift--.f64 N/A

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

   5. remove-double-neg N/A

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

   6. div-inv N/A

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

   7. lift-*.f64 N/A

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

   8. div-inv N/A

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

   9. lift-*.f64 N/A

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

   10. *-commutative N/A

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

   11. associate-/l* N/A

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

   12. *-commutative N/A

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

   13. lower-fma.f64 N/A

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

   14. lower-/.f64 99.8

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

4. Applied rewrites 99.8%

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

   1. lift--.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. +-commutative N/A

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

   6. lift-*.f64 N/A

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

   7. lower-fma.f64 N/A

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

   8. *-commutative N/A

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

   9. lift-/.f64 N/A

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

   10. clear-num N/A

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

   11. un-div-inv N/A

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

   12. lower-/.f64 N/A

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

   13. div-inv N/A

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

   14. lower-*.f64 N/A

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

   15. metadata-eval 99.8

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

6. Applied rewrites 99.8%

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

Alternative 2: 59.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot 60\\ t_2 := \frac{t\_1}{z}\\ t_3 := \frac{t\_1}{z - t}\\ \mathbf{if}\;t\_3 \leq -3 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+28}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{+251}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot -60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- x y) 60.0)) (t_2 (/ t_1 z)) (t_3 (/ t_1 (- z t))))
   (if (<= t_3 -3e+26)
     t_2
     (if (<= t_3 2e+28)
       (* a 120.0)
       (if (<= t_3 4e+251) t_2 (/ (* (- x y) -60.0) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) * 60.0;
	double t_2 = t_1 / z;
	double t_3 = t_1 / (z - t);
	double tmp;
	if (t_3 <= -3e+26) {
		tmp = t_2;
	} else if (t_3 <= 2e+28) {
		tmp = a * 120.0;
	} else if (t_3 <= 4e+251) {
		tmp = t_2;
	} else {
		tmp = ((x - y) * -60.0) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x - y) * 60.0d0
    t_2 = t_1 / z
    t_3 = t_1 / (z - t)
    if (t_3 <= (-3d+26)) then
        tmp = t_2
    else if (t_3 <= 2d+28) then
        tmp = a * 120.0d0
    else if (t_3 <= 4d+251) then
        tmp = t_2
    else
        tmp = ((x - y) * (-60.0d0)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) * 60.0;
	double t_2 = t_1 / z;
	double t_3 = t_1 / (z - t);
	double tmp;
	if (t_3 <= -3e+26) {
		tmp = t_2;
	} else if (t_3 <= 2e+28) {
		tmp = a * 120.0;
	} else if (t_3 <= 4e+251) {
		tmp = t_2;
	} else {
		tmp = ((x - y) * -60.0) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - y) * 60.0
	t_2 = t_1 / z
	t_3 = t_1 / (z - t)
	tmp = 0
	if t_3 <= -3e+26:
		tmp = t_2
	elif t_3 <= 2e+28:
		tmp = a * 120.0
	elif t_3 <= 4e+251:
		tmp = t_2
	else:
		tmp = ((x - y) * -60.0) / t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) * 60.0)
	t_2 = Float64(t_1 / z)
	t_3 = Float64(t_1 / Float64(z - t))
	tmp = 0.0
	if (t_3 <= -3e+26)
		tmp = t_2;
	elseif (t_3 <= 2e+28)
		tmp = Float64(a * 120.0);
	elseif (t_3 <= 4e+251)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(x - y) * -60.0) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - y) * 60.0;
	t_2 = t_1 / z;
	t_3 = t_1 / (z - t);
	tmp = 0.0;
	if (t_3 <= -3e+26)
		tmp = t_2;
	elseif (t_3 <= 2e+28)
		tmp = a * 120.0;
	elseif (t_3 <= 4e+251)
		tmp = t_2;
	else
		tmp = ((x - y) * -60.0) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / z), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -3e+26], t$95$2, If[LessEqual[t$95$3, 2e+28], N[(a * 120.0), $MachinePrecision], If[LessEqual[t$95$3, 4e+251], t$95$2, N[(N[(N[(x - y), $MachinePrecision] * -60.0), $MachinePrecision] / t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.99999999999999997e26 or 1.99999999999999992e28 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.0000000000000002e251

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 64.7

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

   5. Applied rewrites 64.7%

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

   6. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 51.3

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

   8. Applied rewrites 51.3%

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

   if -2.99999999999999997e26 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.99999999999999992e28

   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 73.2

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

   5. Applied rewrites 73.2%

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

   if 4.0000000000000002e251 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 81.9

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

   5. Applied rewrites 81.9%

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

   6. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 81.9

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

   8. Applied rewrites 81.9%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -3 \cdot 10^{+26}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+28}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 4 \cdot 10^{+251}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot -60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ t_2 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+202}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+28}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))) (t_2 (* 60.0 (/ x (- z t)))))
   (if (<= t_1 -2e+202)
     (* -60.0 (/ y (- z t)))
     (if (<= t_1 -1e+28) t_2 (if (<= t_1 2e+28) (* a 120.0) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double t_2 = 60.0 * (x / (z - t));
	double tmp;
	if (t_1 <= -2e+202) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_1 <= -1e+28) {
		tmp = t_2;
	} else if (t_1 <= 2e+28) {
		tmp = a * 120.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x - y) * 60.0d0) / (z - t)
    t_2 = 60.0d0 * (x / (z - t))
    if (t_1 <= (-2d+202)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (t_1 <= (-1d+28)) then
        tmp = t_2
    else if (t_1 <= 2d+28) then
        tmp = a * 120.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double t_2 = 60.0 * (x / (z - t));
	double tmp;
	if (t_1 <= -2e+202) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_1 <= -1e+28) {
		tmp = t_2;
	} else if (t_1 <= 2e+28) {
		tmp = a * 120.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	t_2 = 60.0 * (x / (z - t))
	tmp = 0
	if t_1 <= -2e+202:
		tmp = -60.0 * (y / (z - t))
	elif t_1 <= -1e+28:
		tmp = t_2
	elif t_1 <= 2e+28:
		tmp = a * 120.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	t_2 = Float64(60.0 * Float64(x / Float64(z - t)))
	tmp = 0.0
	if (t_1 <= -2e+202)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (t_1 <= -1e+28)
		tmp = t_2;
	elseif (t_1 <= 2e+28)
		tmp = Float64(a * 120.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) * 60.0) / (z - t);
	t_2 = 60.0 * (x / (z - t));
	tmp = 0.0;
	if (t_1 <= -2e+202)
		tmp = -60.0 * (y / (z - t));
	elseif (t_1 <= -1e+28)
		tmp = t_2;
	elseif (t_1 <= 2e+28)
		tmp = a * 120.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+202], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e+28], t$95$2, If[LessEqual[t$95$1, 2e+28], N[(a * 120.0), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.9999999999999998e202

   1. Initial program 95.1%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 65.8

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

   5. Applied rewrites 65.8%

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

   if -1.9999999999999998e202 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.99999999999999958e27 or 1.99999999999999992e28 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.7%

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

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 51.3

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

   5. Applied rewrites 51.3%

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

      1. lift--.f64 N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 52.4

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

   7. Applied rewrites 52.4%

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

   if -9.99999999999999958e27 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.99999999999999992e28

   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 72.7

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

   5. Applied rewrites 72.7%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+202}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{+28}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+28}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -3 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-77}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -3e+26) t_1 (if (<= t_1 4e-77) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -3e+26) {
		tmp = t_1;
	} else if (t_1 <= 4e-77) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x - y) * 60.0d0) / (z - t)
    if (t_1 <= (-3d+26)) then
        tmp = t_1
    else if (t_1 <= 4d-77) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -3e+26) {
		tmp = t_1;
	} else if (t_1 <= 4e-77) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_1 <= -3e+26:
		tmp = t_1
	elif t_1 <= 4e-77:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -3e+26)
		tmp = t_1;
	elseif (t_1 <= 4e-77)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_1 <= -3e+26)
		tmp = t_1;
	elseif (t_1 <= 4e-77)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -3e+26], t$95$1, If[LessEqual[t$95$1, 4e-77], N[(a * 120.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.99999999999999997e26 or 3.9999999999999997e-77 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.4%

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

   3. Taylor expanded in a around 0

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

      1. 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. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 77.2

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

   5. Applied rewrites 77.2%

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

   if -2.99999999999999997e26 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 3.9999999999999997e-77

   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 80.0

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

   5. Applied rewrites 80.0%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -3 \cdot 10^{+26}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 4 \cdot 10^{-77}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+170}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+109}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -2e+170)
     (* -60.0 (/ y z))
     (if (<= t_1 1e+109) (* a 120.0) (/ (* x 60.0) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -2e+170) {
		tmp = -60.0 * (y / z);
	} else if (t_1 <= 1e+109) {
		tmp = a * 120.0;
	} else {
		tmp = (x * 60.0) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x - y) * 60.0d0) / (z - t)
    if (t_1 <= (-2d+170)) then
        tmp = (-60.0d0) * (y / z)
    else if (t_1 <= 1d+109) then
        tmp = a * 120.0d0
    else
        tmp = (x * 60.0d0) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -2e+170) {
		tmp = -60.0 * (y / z);
	} else if (t_1 <= 1e+109) {
		tmp = a * 120.0;
	} else {
		tmp = (x * 60.0) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_1 <= -2e+170:
		tmp = -60.0 * (y / z)
	elif t_1 <= 1e+109:
		tmp = a * 120.0
	else:
		tmp = (x * 60.0) / z
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+170)
		tmp = Float64(-60.0 * Float64(y / z));
	elseif (t_1 <= 1e+109)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(x * 60.0) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+170)
		tmp = -60.0 * (y / z);
	elseif (t_1 <= 1e+109)
		tmp = a * 120.0;
	else
		tmp = (x * 60.0) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+170], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+109], N[(a * 120.0), $MachinePrecision], N[(N[(x * 60.0), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.00000000000000007e170

   1. Initial program 96.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 60.7

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

   5. Applied rewrites 60.7%

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

   6. Taylor expanded in z around inf

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

      1. lower-/.f64 56.7

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

   8. Applied rewrites 56.7%

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

   if -2.00000000000000007e170 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999982e108

   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 62.2

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

   5. Applied rewrites 62.2%

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

   if 9.99999999999999982e108 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 48.9

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

   5. Applied rewrites 48.9%

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

   6. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 34.9

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

   8. Applied rewrites 34.9%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+170}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{+109}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+170}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+211}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -2e+170)
     (* -60.0 (/ y z))
     (if (<= t_1 2e+211) (* a 120.0) (/ (* x -60.0) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -2e+170) {
		tmp = -60.0 * (y / z);
	} else if (t_1 <= 2e+211) {
		tmp = a * 120.0;
	} else {
		tmp = (x * -60.0) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x - y) * 60.0d0) / (z - t)
    if (t_1 <= (-2d+170)) then
        tmp = (-60.0d0) * (y / z)
    else if (t_1 <= 2d+211) then
        tmp = a * 120.0d0
    else
        tmp = (x * (-60.0d0)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -2e+170) {
		tmp = -60.0 * (y / z);
	} else if (t_1 <= 2e+211) {
		tmp = a * 120.0;
	} else {
		tmp = (x * -60.0) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_1 <= -2e+170:
		tmp = -60.0 * (y / z)
	elif t_1 <= 2e+211:
		tmp = a * 120.0
	else:
		tmp = (x * -60.0) / t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+170)
		tmp = Float64(-60.0 * Float64(y / z));
	elseif (t_1 <= 2e+211)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(x * -60.0) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+170)
		tmp = -60.0 * (y / z);
	elseif (t_1 <= 2e+211)
		tmp = a * 120.0;
	else
		tmp = (x * -60.0) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+170], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+211], N[(a * 120.0), $MachinePrecision], N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.00000000000000007e170

   1. Initial program 96.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 60.7

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

   5. Applied rewrites 60.7%

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

   6. Taylor expanded in z around inf

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

      1. lower-/.f64 56.7

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

   8. Applied rewrites 56.7%

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

   if -2.00000000000000007e170 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.9999999999999999e211

   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 58.1

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

   5. Applied rewrites 58.1%

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

   if 1.9999999999999999e211 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 55.6

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

   5. Applied rewrites 55.6%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 44.1

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

   8. Applied rewrites 44.1%

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 44.2

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

   10. Applied rewrites 44.2%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+170}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+211}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+170}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+211}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -2e+170)
     (* -60.0 (/ y z))
     (if (<= t_1 2e+211) (* a 120.0) (* -60.0 (/ x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -2e+170) {
		tmp = -60.0 * (y / z);
	} else if (t_1 <= 2e+211) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x - y) * 60.0d0) / (z - t)
    if (t_1 <= (-2d+170)) then
        tmp = (-60.0d0) * (y / z)
    else if (t_1 <= 2d+211) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -2e+170) {
		tmp = -60.0 * (y / z);
	} else if (t_1 <= 2e+211) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_1 <= -2e+170:
		tmp = -60.0 * (y / z)
	elif t_1 <= 2e+211:
		tmp = a * 120.0
	else:
		tmp = -60.0 * (x / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+170)
		tmp = Float64(-60.0 * Float64(y / z));
	elseif (t_1 <= 2e+211)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+170)
		tmp = -60.0 * (y / z);
	elseif (t_1 <= 2e+211)
		tmp = a * 120.0;
	else
		tmp = -60.0 * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+170], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+211], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.00000000000000007e170

   1. Initial program 96.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 60.7

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

   5. Applied rewrites 60.7%

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

   6. Taylor expanded in z around inf

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

      1. lower-/.f64 56.7

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

   8. Applied rewrites 56.7%

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

   if -2.00000000000000007e170 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.9999999999999999e211

   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 58.1

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

   5. Applied rewrites 58.1%

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

   if 1.9999999999999999e211 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 55.6

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

   5. Applied rewrites 55.6%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 44.1

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

   8. Applied rewrites 44.1%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+170}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+211}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x}{t}\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+211}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ x t))) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -1e+28) t_1 (if (<= t_2 2e+211) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (x / t);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -1e+28) {
		tmp = t_1;
	} else if (t_2 <= 2e+211) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-60.0d0) * (x / t)
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-1d+28)) then
        tmp = t_1
    else if (t_2 <= 2d+211) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (x / t);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -1e+28) {
		tmp = t_1;
	} else if (t_2 <= 2e+211) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (x / t)
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -1e+28:
		tmp = t_1
	elif t_2 <= 2e+211:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(x / t))
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+28)
		tmp = t_1;
	elseif (t_2 <= 2e+211)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (x / t);
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+28)
		tmp = t_1;
	elseif (t_2 <= 2e+211)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+28], t$95$1, If[LessEqual[t$95$2, 2e+211], N[(a * 120.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.99999999999999958e27 or 1.9999999999999999e211 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.0%

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

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 49.6

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

   5. Applied rewrites 49.6%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 31.7

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

   8. Applied rewrites 31.7%

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

   if -9.99999999999999958e27 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.9999999999999999e211

   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 62.7

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

   5. Applied rewrites 62.7%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{+28}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+211}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 120, \frac{x - y}{t \cdot -0.016666666666666666}\right)\\ \mathbf{if}\;t \leq -9.6 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma a 120.0 (/ (- x y) (* t -0.016666666666666666)))))
   (if (<= t -9.6e+57)
     t_1
     (if (<= t 1.2e-7) (fma 60.0 (/ (- x y) z) (* a 120.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(a, 120.0, ((x - y) / (t * -0.016666666666666666)));
	double tmp;
	if (t <= -9.6e+57) {
		tmp = t_1;
	} else if (t <= 1.2e-7) {
		tmp = fma(60.0, ((x - y) / z), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(a, 120.0, Float64(Float64(x - y) / Float64(t * -0.016666666666666666)))
	tmp = 0.0
	if (t <= -9.6e+57)
		tmp = t_1;
	elseif (t <= 1.2e-7)
		tmp = fma(60.0, Float64(Float64(x - y) / z), Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a * 120.0 + N[(N[(x - y), $MachinePrecision] / N[(t * -0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.6e+57], t$95$1, If[LessEqual[t, 1.2e-7], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -9.60000000000000019e57 or 1.19999999999999989e-7 < t

   1. Initial program 99.8%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. div-inv N/A

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

      7. lift-*.f64 N/A

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

      8. div-inv N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-/.f64 N/A

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

      10. clear-num N/A

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

      11. un-div-inv N/A

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

      12. lower-/.f64 N/A

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

      13. div-inv N/A

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

      14. lower-*.f64 N/A

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

      15. metadata-eval 99.9

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

   6. Applied rewrites 99.9%

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

   7. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 91.9

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

   9. Applied rewrites 91.9%

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

   if -9.60000000000000019e57 < t < 1.19999999999999989e-7

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 85.1

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

   5. Applied rewrites 85.1%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{+57}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{t \cdot -0.016666666666666666}\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{t \cdot -0.016666666666666666}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{t}\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, -60 \cdot t\_1\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, t\_1, a \cdot 120\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x y) t)))
   (if (<= t -2.4e+113)
     (fma a 120.0 (* -60.0 t_1))
     (if (<= t 1.2e-7)
       (fma 60.0 (/ (- x y) z) (* a 120.0))
       (fma -60.0 t_1 (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) / t;
	double tmp;
	if (t <= -2.4e+113) {
		tmp = fma(a, 120.0, (-60.0 * t_1));
	} else if (t <= 1.2e-7) {
		tmp = fma(60.0, ((x - y) / z), (a * 120.0));
	} else {
		tmp = fma(-60.0, t_1, (a * 120.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) / t)
	tmp = 0.0
	if (t <= -2.4e+113)
		tmp = fma(a, 120.0, Float64(-60.0 * t_1));
	elseif (t <= 1.2e-7)
		tmp = fma(60.0, Float64(Float64(x - y) / z), Float64(a * 120.0));
	else
		tmp = fma(-60.0, t_1, Float64(a * 120.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -2.4e+113], N[(a * 120.0 + N[(-60.0 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-7], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(-60.0 * t$95$1 + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.39999999999999983e113

   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

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 93.7

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

   5. Applied rewrites 93.7%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 93.8

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

   7. Applied rewrites 93.8%

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

   if -2.39999999999999983e113 < t < 1.19999999999999989e-7

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 84.0

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

   5. Applied rewrites 84.0%

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

   if 1.19999999999999989e-7 < t

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 95.0

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

   5. Applied rewrites 95.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, -60 \cdot \frac{x - y}{t}\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 82.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma -60.0 (/ (- x y) t) (* a 120.0))))
   (if (<= t -2.4e+113)
     t_1
     (if (<= t 1.2e-7) (fma 60.0 (/ (- x y) z) (* a 120.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-60.0, ((x - y) / t), (a * 120.0));
	double tmp;
	if (t <= -2.4e+113) {
		tmp = t_1;
	} else if (t <= 1.2e-7) {
		tmp = fma(60.0, ((x - y) / z), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(-60.0, Float64(Float64(x - y) / t), Float64(a * 120.0))
	tmp = 0.0
	if (t <= -2.4e+113)
		tmp = t_1;
	elseif (t <= 1.2e-7)
		tmp = fma(60.0, Float64(Float64(x - y) / z), Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.4e+113], t$95$1, If[LessEqual[t, 1.2e-7], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.39999999999999983e113 or 1.19999999999999989e-7 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 94.5

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

   5. Applied rewrites 94.5%

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

   if -2.39999999999999983e113 < t < 1.19999999999999989e-7

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 84.0

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

   5. Applied rewrites 84.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 82.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;y \leq -1.78 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+129}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z - t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= y -1.78e+137)
     t_1
     (if (<= y 2.35e+129) (fma 60.0 (/ x (- z t)) (* a 120.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (y <= -1.78e+137) {
		tmp = t_1;
	} else if (y <= 2.35e+129) {
		tmp = fma(60.0, (x / (z - t)), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (y <= -1.78e+137)
		tmp = t_1;
	elseif (y <= 2.35e+129)
		tmp = fma(60.0, Float64(x / Float64(z - t)), Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.78e+137], t$95$1, If[LessEqual[y, 2.35e+129], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.77999999999999997e137 or 2.35000000000000004e129 < y

   1. Initial program 97.2%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 75.0

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

   5. Applied rewrites 75.0%

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

   if -1.77999999999999997e137 < y < 2.35000000000000004e129

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 92.3

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

   5. Applied rewrites 92.3%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.78 \cdot 10^{+137}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+129}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z - t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -1.78 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+132}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))))
   (if (<= y -1.78e+137) t_1 (if (<= y 4.5e+132) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -1.78e+137) {
		tmp = t_1;
	} else if (y <= 4.5e+132) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * (y / (z - t))
    if (y <= (-1.78d+137)) then
        tmp = t_1
    else if (y <= 4.5d+132) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -1.78e+137) {
		tmp = t_1;
	} else if (y <= 4.5e+132) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	tmp = 0
	if y <= -1.78e+137:
		tmp = t_1
	elif y <= 4.5e+132:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	tmp = 0.0
	if (y <= -1.78e+137)
		tmp = t_1;
	elseif (y <= 4.5e+132)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (y / (z - t));
	tmp = 0.0;
	if (y <= -1.78e+137)
		tmp = t_1;
	elseif (y <= 4.5e+132)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.78e+137], t$95$1, If[LessEqual[y, 4.5e+132], N[(a * 120.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.77999999999999997e137 or 4.49999999999999972e132 < y

   1. Initial program 97.1%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 64.7

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

   5. Applied rewrites 64.7%

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

   if -1.77999999999999997e137 < y < 4.49999999999999972e132

   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 58.9

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

   5. Applied rewrites 58.9%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.78 \cdot 10^{+137}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+132}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 99.3% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

   1. lift--.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. remove-double-neg N/A

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

   4. lift--.f64 N/A

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

   5. remove-double-neg N/A

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

   6. lift-/.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. +-commutative N/A

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

   9. lift-*.f64 N/A

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

   10. lower-fma.f64 99.1

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

   11. lift-/.f64 N/A

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

   12. frac-2neg N/A

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

   13. lower-/.f64 N/A

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

   14. lift-*.f64 N/A

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

   15. *-commutative N/A

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

   16. distribute-rgt-neg-in N/A

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

   17. lower-*.f64 N/A

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

   18. metadata-eval N/A

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

   19. neg-sub0 N/A

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

   20. lift--.f64 N/A

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

   21. sub-neg N/A

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

   22. +-commutative N/A

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

   23. associate--r+ N/A

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

   24. neg-sub0 N/A

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

   25. remove-double-neg N/A

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

   26. lower--.f64 99.1

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

4. Applied rewrites 99.1%

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

Alternative 15: 51.1% accurate, 5.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

3. Taylor expanded in z around inf

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

   1. lower-*.f64 49.2

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

5. Applied rewrites 49.2%

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

6. Final simplification 49.2%

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

Developer Target 1: 99.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024216 
(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)))