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

Percentage Accurate: 99.4% → 99.8%

Time: 15.1s

Alternatives: 20

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

   1. *-commutative 99.0%

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

   2. associate-/l* 99.4%

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

   3. fma-define 99.4%

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

   4. sub-neg 99.4%

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

   5. +-commutative 99.4%

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

   6. neg-sub0 99.4%

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

   7. associate-+l- 99.4%

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

   8. sub0-neg 99.4%

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

   9. distribute-frac-neg2 99.4%

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

   10. distribute-neg-frac 99.4%

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

   11. metadata-eval 99.4%

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

3. Simplified 99.4%

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

5. Final simplification 99.4%

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

Alternative 2: 53.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{-60}{t}\\ t_2 := 60 \cdot \frac{x - y}{z}\\ \mathbf{if}\;x - y \leq -4 \cdot 10^{+177}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x - y \leq -4 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x - y \leq 2 \cdot 10^{+204}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x - y \leq 10^{+236}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ -60.0 t))) (t_2 (* 60.0 (/ (- x y) z))))
   (if (<= (- x y) -4e+177)
     t_2
     (if (<= (- x y) -4e+100)
       t_1
       (if (<= (- x y) 2e+204)
         (* a 120.0)
         (if (<= (- x y) 1e+236) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) * (-60.0 / t);
	double t_2 = 60.0 * ((x - y) / z);
	double tmp;
	if ((x - y) <= -4e+177) {
		tmp = t_2;
	} else if ((x - y) <= -4e+100) {
		tmp = t_1;
	} else if ((x - y) <= 2e+204) {
		tmp = a * 120.0;
	} else if ((x - y) <= 1e+236) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) * ((-60.0d0) / t)
    t_2 = 60.0d0 * ((x - y) / z)
    if ((x - y) <= (-4d+177)) then
        tmp = t_2
    else if ((x - y) <= (-4d+100)) then
        tmp = t_1
    else if ((x - y) <= 2d+204) then
        tmp = a * 120.0d0
    else if ((x - y) <= 1d+236) then
        tmp = t_2
    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 / t);
	double t_2 = 60.0 * ((x - y) / z);
	double tmp;
	if ((x - y) <= -4e+177) {
		tmp = t_2;
	} else if ((x - y) <= -4e+100) {
		tmp = t_1;
	} else if ((x - y) <= 2e+204) {
		tmp = a * 120.0;
	} else if ((x - y) <= 1e+236) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - y) * (-60.0 / t)
	t_2 = 60.0 * ((x - y) / z)
	tmp = 0
	if (x - y) <= -4e+177:
		tmp = t_2
	elif (x - y) <= -4e+100:
		tmp = t_1
	elif (x - y) <= 2e+204:
		tmp = a * 120.0
	elif (x - y) <= 1e+236:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) * Float64(-60.0 / t))
	t_2 = Float64(60.0 * Float64(Float64(x - y) / z))
	tmp = 0.0
	if (Float64(x - y) <= -4e+177)
		tmp = t_2;
	elseif (Float64(x - y) <= -4e+100)
		tmp = t_1;
	elseif (Float64(x - y) <= 2e+204)
		tmp = Float64(a * 120.0);
	elseif (Float64(x - y) <= 1e+236)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - y) * (-60.0 / t);
	t_2 = 60.0 * ((x - y) / z);
	tmp = 0.0;
	if ((x - y) <= -4e+177)
		tmp = t_2;
	elseif ((x - y) <= -4e+100)
		tmp = t_1;
	elseif ((x - y) <= 2e+204)
		tmp = a * 120.0;
	elseif ((x - y) <= 1e+236)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x - y), $MachinePrecision], -4e+177], t$95$2, If[LessEqual[N[(x - y), $MachinePrecision], -4e+100], t$95$1, If[LessEqual[N[(x - y), $MachinePrecision], 2e+204], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(x - y), $MachinePrecision], 1e+236], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 x y) < -4e177 or 1.99999999999999998e204 < (-.f64 x y) < 1.00000000000000005e236

   1. Initial program 97.1%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in a around 0 76.4%

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

      1. associate-*r/ 75.2%

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

      2. *-rgt-identity 75.2%

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

      3. times-frac 76.4%

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

      4. /-rgt-identity 76.4%

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

   7. Simplified 76.4%

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

      1. clear-num 76.3%

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

      2. inv-pow 76.3%

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

      3. div-inv 76.4%

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

      4. metadata-eval 76.4%

         \[\leadsto {\left(\left(z - t\right) \cdot \color{blue}{0.016666666666666666}\right)}^{-1} \cdot \left(x - y\right) \]

   9. Applied egg-rr 76.4%

      \[\leadsto \color{blue}{{\left(\left(z - t\right) \cdot 0.016666666666666666\right)}^{-1}} \cdot \left(x - y\right) \]
   10. Step-by-step derivation

       1. unpow-1 76.4%

          \[\leadsto \color{blue}{\frac{1}{\left(z - t\right) \cdot 0.016666666666666666}} \cdot \left(x - y\right) \]

   11. Simplified 76.4%

       \[\leadsto \color{blue}{\frac{1}{\left(z - t\right) \cdot 0.016666666666666666}} \cdot \left(x - y\right) \]

   12. Taylor expanded in z around inf 53.6%

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

   if -4e177 < (-.f64 x y) < -4.00000000000000006e100 or 1.00000000000000005e236 < (-.f64 x y)

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 80.6%

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

      1. associate-*r/ 80.6%

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

      2. *-rgt-identity 80.6%

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

      3. times-frac 80.5%

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

      4. /-rgt-identity 80.5%

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

   7. Simplified 80.5%

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

   8. Taylor expanded in z around 0 62.1%

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

   if -4.00000000000000006e100 < (-.f64 x y) < 1.99999999999999998e204

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 67.1%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - y \leq -4 \cdot 10^{+177}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;x - y \leq -4 \cdot 10^{+100}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;x - y \leq 2 \cdot 10^{+204}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x - y \leq 10^{+236}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot -60}{t}\\ \mathbf{if}\;x - y \leq -4 \cdot 10^{+177}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;x - y \leq -4 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x - y \leq 2 \cdot 10^{+204}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x - y \leq 10^{+236}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) -60.0) t)))
   (if (<= (- x y) -4e+177)
     (* (- x y) (/ 60.0 z))
     (if (<= (- x y) -4e+100)
       t_1
       (if (<= (- x y) 2e+204)
         (* a 120.0)
         (if (<= (- x y) 1e+236) (* 60.0 (/ (- x y) z)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * -60.0) / t;
	double tmp;
	if ((x - y) <= -4e+177) {
		tmp = (x - y) * (60.0 / z);
	} else if ((x - y) <= -4e+100) {
		tmp = t_1;
	} else if ((x - y) <= 2e+204) {
		tmp = a * 120.0;
	} else if ((x - y) <= 1e+236) {
		tmp = 60.0 * ((x - y) / z);
	} 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)) / t
    if ((x - y) <= (-4d+177)) then
        tmp = (x - y) * (60.0d0 / z)
    else if ((x - y) <= (-4d+100)) then
        tmp = t_1
    else if ((x - y) <= 2d+204) then
        tmp = a * 120.0d0
    else if ((x - y) <= 1d+236) then
        tmp = 60.0d0 * ((x - y) / z)
    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) / t;
	double tmp;
	if ((x - y) <= -4e+177) {
		tmp = (x - y) * (60.0 / z);
	} else if ((x - y) <= -4e+100) {
		tmp = t_1;
	} else if ((x - y) <= 2e+204) {
		tmp = a * 120.0;
	} else if ((x - y) <= 1e+236) {
		tmp = 60.0 * ((x - y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * -60.0) / t
	tmp = 0
	if (x - y) <= -4e+177:
		tmp = (x - y) * (60.0 / z)
	elif (x - y) <= -4e+100:
		tmp = t_1
	elif (x - y) <= 2e+204:
		tmp = a * 120.0
	elif (x - y) <= 1e+236:
		tmp = 60.0 * ((x - y) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * -60.0) / t)
	tmp = 0.0
	if (Float64(x - y) <= -4e+177)
		tmp = Float64(Float64(x - y) * Float64(60.0 / z));
	elseif (Float64(x - y) <= -4e+100)
		tmp = t_1;
	elseif (Float64(x - y) <= 2e+204)
		tmp = Float64(a * 120.0);
	elseif (Float64(x - y) <= 1e+236)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) * -60.0) / t;
	tmp = 0.0;
	if ((x - y) <= -4e+177)
		tmp = (x - y) * (60.0 / z);
	elseif ((x - y) <= -4e+100)
		tmp = t_1;
	elseif ((x - y) <= 2e+204)
		tmp = a * 120.0;
	elseif ((x - y) <= 1e+236)
		tmp = 60.0 * ((x - y) / z);
	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] / t), $MachinePrecision]}, If[LessEqual[N[(x - y), $MachinePrecision], -4e+177], N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x - y), $MachinePrecision], -4e+100], t$95$1, If[LessEqual[N[(x - y), $MachinePrecision], 2e+204], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(x - y), $MachinePrecision], 1e+236], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 x y) < -4e177

   1. Initial program 96.5%

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

      1. associate-/l* 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in a around 0 76.2%

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

      1. associate-*r/ 74.6%

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

      2. *-rgt-identity 74.6%

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

      3. times-frac 76.1%

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

      4. /-rgt-identity 76.1%

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

   7. Simplified 76.1%

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

   8. Taylor expanded in z around inf 48.7%

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

   if -4e177 < (-.f64 x y) < -4.00000000000000006e100 or 1.00000000000000005e236 < (-.f64 x y)

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 80.6%

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

      1. associate-*r/ 80.6%

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

      2. *-rgt-identity 80.6%

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

      3. times-frac 80.5%

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

      4. /-rgt-identity 80.5%

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

   7. Simplified 80.5%

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

   8. Taylor expanded in z around 0 62.1%

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

      1. associate-*l/ 62.2%

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

   10. Applied egg-rr 62.2%

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

   if -4.00000000000000006e100 < (-.f64 x y) < 1.99999999999999998e204

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 67.1%

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

   if 1.99999999999999998e204 < (-.f64 x y) < 1.00000000000000005e236

   1. Initial program 99.9%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 77.5%

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

      1. associate-*r/ 77.8%

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

      2. *-rgt-identity 77.8%

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

      3. times-frac 77.5%

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

      4. /-rgt-identity 77.5%

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

   7. Simplified 77.5%

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

      1. clear-num 77.7%

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

      2. inv-pow 77.7%

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

      3. div-inv 77.7%

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

      4. metadata-eval 77.7%

         \[\leadsto {\left(\left(z - t\right) \cdot \color{blue}{0.016666666666666666}\right)}^{-1} \cdot \left(x - y\right) \]

   9. Applied egg-rr 77.7%

      \[\leadsto \color{blue}{{\left(\left(z - t\right) \cdot 0.016666666666666666\right)}^{-1}} \cdot \left(x - y\right) \]
   10. Step-by-step derivation

       1. unpow-1 77.7%

          \[\leadsto \color{blue}{\frac{1}{\left(z - t\right) \cdot 0.016666666666666666}} \cdot \left(x - y\right) \]

   11. Simplified 77.7%

       \[\leadsto \color{blue}{\frac{1}{\left(z - t\right) \cdot 0.016666666666666666}} \cdot \left(x - y\right) \]

   12. Taylor expanded in z around inf 77.7%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - y \leq -4 \cdot 10^{+177}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;x - y \leq -4 \cdot 10^{+100}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot -60}{t}\\ \mathbf{elif}\;x - y \leq 2 \cdot 10^{+204}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x - y \leq 10^{+236}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot -60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ t_2 := a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-197}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+76}:\\ \;\;\;\;\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* -60.0 (/ (- x y) t))))
        (t_2 (+ (* a 120.0) (* 60.0 (/ x z)))))
   (if (<= z -7e+81)
     t_2
     (if (<= z -2.4e-90)
       t_1
       (if (<= z -1.8e-197)
         (* 60.0 (/ (- x y) (- z t)))
         (if (<= z 3.8e-97)
           t_1
           (if (<= z 2.6e+76)
             (/ (- x y) (* (- z t) 0.016666666666666666))
             t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (-60.0 * ((x - y) / t));
	double t_2 = (a * 120.0) + (60.0 * (x / z));
	double tmp;
	if (z <= -7e+81) {
		tmp = t_2;
	} else if (z <= -2.4e-90) {
		tmp = t_1;
	} else if (z <= -1.8e-197) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (z <= 3.8e-97) {
		tmp = t_1;
	} else if (z <= 2.6e+76) {
		tmp = (x - y) / ((z - t) * 0.016666666666666666);
	} 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 = (a * 120.0d0) + ((-60.0d0) * ((x - y) / t))
    t_2 = (a * 120.0d0) + (60.0d0 * (x / z))
    if (z <= (-7d+81)) then
        tmp = t_2
    else if (z <= (-2.4d-90)) then
        tmp = t_1
    else if (z <= (-1.8d-197)) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if (z <= 3.8d-97) then
        tmp = t_1
    else if (z <= 2.6d+76) then
        tmp = (x - y) / ((z - t) * 0.016666666666666666d0)
    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 = (a * 120.0) + (-60.0 * ((x - y) / t));
	double t_2 = (a * 120.0) + (60.0 * (x / z));
	double tmp;
	if (z <= -7e+81) {
		tmp = t_2;
	} else if (z <= -2.4e-90) {
		tmp = t_1;
	} else if (z <= -1.8e-197) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (z <= 3.8e-97) {
		tmp = t_1;
	} else if (z <= 2.6e+76) {
		tmp = (x - y) / ((z - t) * 0.016666666666666666);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (-60.0 * ((x - y) / t))
	t_2 = (a * 120.0) + (60.0 * (x / z))
	tmp = 0
	if z <= -7e+81:
		tmp = t_2
	elif z <= -2.4e-90:
		tmp = t_1
	elif z <= -1.8e-197:
		tmp = 60.0 * ((x - y) / (z - t))
	elif z <= 3.8e-97:
		tmp = t_1
	elif z <= 2.6e+76:
		tmp = (x - y) / ((z - t) * 0.016666666666666666)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(Float64(x - y) / t)))
	t_2 = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)))
	tmp = 0.0
	if (z <= -7e+81)
		tmp = t_2;
	elseif (z <= -2.4e-90)
		tmp = t_1;
	elseif (z <= -1.8e-197)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (z <= 3.8e-97)
		tmp = t_1;
	elseif (z <= 2.6e+76)
		tmp = Float64(Float64(x - y) / Float64(Float64(z - t) * 0.016666666666666666));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (-60.0 * ((x - y) / t));
	t_2 = (a * 120.0) + (60.0 * (x / z));
	tmp = 0.0;
	if (z <= -7e+81)
		tmp = t_2;
	elseif (z <= -2.4e-90)
		tmp = t_1;
	elseif (z <= -1.8e-197)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif (z <= 3.8e-97)
		tmp = t_1;
	elseif (z <= 2.6e+76)
		tmp = (x - y) / ((z - t) * 0.016666666666666666);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+81], t$95$2, If[LessEqual[z, -2.4e-90], t$95$1, If[LessEqual[z, -1.8e-197], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-97], t$95$1, If[LessEqual[z, 2.6e+76], N[(N[(x - y), $MachinePrecision] / N[(N[(z - t), $MachinePrecision] * 0.016666666666666666), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.0000000000000001e81 or 2.5999999999999999e76 < z

   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 82.4%

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

   4. Taylor expanded in z around inf 81.1%

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

   if -7.0000000000000001e81 < z < -2.4000000000000002e-90 or -1.7999999999999999e-197 < z < 3.8000000000000001e-97

   1. Initial program 98.9%

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

      1. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in z around 0 92.3%

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

   if -2.4000000000000002e-90 < z < -1.7999999999999999e-197

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 87.5%

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

   if 3.8000000000000001e-97 < z < 2.5999999999999999e76

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 71.4%

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

      1. associate-*r/ 71.2%

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

      2. *-rgt-identity 71.2%

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

      3. times-frac 71.4%

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

      4. /-rgt-identity 71.4%

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

   7. Simplified 71.4%

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

      1. clear-num 71.3%

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

      2. inv-pow 71.3%

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

      3. div-inv 71.3%

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

      4. metadata-eval 71.3%

         \[\leadsto {\left(\left(z - t\right) \cdot \color{blue}{0.016666666666666666}\right)}^{-1} \cdot \left(x - y\right) \]

   9. Applied egg-rr 71.3%

      \[\leadsto \color{blue}{{\left(\left(z - t\right) \cdot 0.016666666666666666\right)}^{-1}} \cdot \left(x - y\right) \]
   10. Step-by-step derivation

       1. unpow-1 71.3%

          \[\leadsto \color{blue}{\frac{1}{\left(z - t\right) \cdot 0.016666666666666666}} \cdot \left(x - y\right) \]

   11. Simplified 71.3%

       \[\leadsto \color{blue}{\frac{1}{\left(z - t\right) \cdot 0.016666666666666666}} \cdot \left(x - y\right) \]
   12. Step-by-step derivation

       1. associate-*l/ 71.4%

          \[\leadsto \color{blue}{\frac{1 \cdot \left(x - y\right)}{\left(z - t\right) \cdot 0.016666666666666666}} \]

       2. *-un-lft-identity 71.4%

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

   13. Applied egg-rr 71.4%

       \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+81}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-90}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-197}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-97}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+76}:\\ \;\;\;\;\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -92 \lor \neg \left(a \leq 1.15 \cdot 10^{-13}\right) \land \left(a \leq 2.25 \cdot 10^{+135} \lor \neg \left(a \leq 5 \cdot 10^{+164}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -92.0)
         (and (not (<= a 1.15e-13)) (or (<= a 2.25e+135) (not (<= a 5e+164)))))
   (* a 120.0)
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -92.0) || (!(a <= 1.15e-13) && ((a <= 2.25e+135) || !(a <= 5e+164)))) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - 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) :: tmp
    if ((a <= (-92.0d0)) .or. (.not. (a <= 1.15d-13)) .and. (a <= 2.25d+135) .or. (.not. (a <= 5d+164))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -92.0) || (!(a <= 1.15e-13) && ((a <= 2.25e+135) || !(a <= 5e+164)))) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -92.0) or (not (a <= 1.15e-13) and ((a <= 2.25e+135) or not (a <= 5e+164))):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -92.0) || (!(a <= 1.15e-13) && ((a <= 2.25e+135) || !(a <= 5e+164))))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -92.0) || (~((a <= 1.15e-13)) && ((a <= 2.25e+135) || ~((a <= 5e+164)))))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -92.0], And[N[Not[LessEqual[a, 1.15e-13]], $MachinePrecision], Or[LessEqual[a, 2.25e+135], N[Not[LessEqual[a, 5e+164]], $MachinePrecision]]]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -92 or 1.1499999999999999e-13 < a < 2.25000000000000004e135 or 4.9999999999999995e164 < a

   1. Initial program 98.3%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in z around inf 71.7%

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

   if -92 < a < 1.1499999999999999e-13 or 2.25000000000000004e135 < a < 4.9999999999999995e164

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 82.8%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -92 \lor \neg \left(a \leq 1.15 \cdot 10^{-13}\right) \land \left(a \leq 2.25 \cdot 10^{+135} \lor \neg \left(a \leq 5 \cdot 10^{+164}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -20 \lor \neg \left(a \leq 2.9 \cdot 10^{-13} \lor \neg \left(a \leq 2.25 \cdot 10^{+135}\right) \land a \leq 1.95 \cdot 10^{+164}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -20.0)
         (not
          (or (<= a 2.9e-13) (and (not (<= a 2.25e+135)) (<= a 1.95e+164)))))
   (* a 120.0)
   (* (- x y) (/ 60.0 (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -20.0) || !((a <= 2.9e-13) || (!(a <= 2.25e+135) && (a <= 1.95e+164)))) {
		tmp = a * 120.0;
	} else {
		tmp = (x - y) * (60.0 / (z - 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) :: tmp
    if ((a <= (-20.0d0)) .or. (.not. (a <= 2.9d-13) .or. (.not. (a <= 2.25d+135)) .and. (a <= 1.95d+164))) then
        tmp = a * 120.0d0
    else
        tmp = (x - y) * (60.0d0 / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -20.0) || !((a <= 2.9e-13) || (!(a <= 2.25e+135) && (a <= 1.95e+164)))) {
		tmp = a * 120.0;
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -20.0) or not ((a <= 2.9e-13) or (not (a <= 2.25e+135) and (a <= 1.95e+164))):
		tmp = a * 120.0
	else:
		tmp = (x - y) * (60.0 / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -20.0) || !((a <= 2.9e-13) || (!(a <= 2.25e+135) && (a <= 1.95e+164))))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -20.0) || ~(((a <= 2.9e-13) || (~((a <= 2.25e+135)) && (a <= 1.95e+164)))))
		tmp = a * 120.0;
	else
		tmp = (x - y) * (60.0 / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -20.0], N[Not[Or[LessEqual[a, 2.9e-13], And[N[Not[LessEqual[a, 2.25e+135]], $MachinePrecision], LessEqual[a, 1.95e+164]]]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -20 or 2.8999999999999998e-13 < a < 2.25000000000000004e135 or 1.94999999999999993e164 < a

   1. Initial program 98.3%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in z around inf 71.7%

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

   if -20 < a < 2.8999999999999998e-13 or 2.25000000000000004e135 < a < 1.94999999999999993e164

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 82.8%

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

      1. associate-*r/ 82.8%

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

      2. *-rgt-identity 82.8%

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

      3. times-frac 82.8%

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

      4. /-rgt-identity 82.8%

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

   7. Simplified 82.8%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -20 \lor \neg \left(a \leq 2.9 \cdot 10^{-13} \lor \neg \left(a \leq 2.25 \cdot 10^{+135}\right) \land a \leq 1.95 \cdot 10^{+164}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -7.4 \cdot 10^{-121}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-289}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-235}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-41}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ x (- z t)))))
   (if (<= a -7.4e-121)
     (* a 120.0)
     (if (<= a -1.65e-289)
       t_1
       (if (<= a 1.25e-235)
         (* 60.0 (/ y (- t z)))
         (if (<= a 2.3e-41) t_1 (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double tmp;
	if (a <= -7.4e-121) {
		tmp = a * 120.0;
	} else if (a <= -1.65e-289) {
		tmp = t_1;
	} else if (a <= 1.25e-235) {
		tmp = 60.0 * (y / (t - z));
	} else if (a <= 2.3e-41) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * (x / (z - t))
    if (a <= (-7.4d-121)) then
        tmp = a * 120.0d0
    else if (a <= (-1.65d-289)) then
        tmp = t_1
    else if (a <= 1.25d-235) then
        tmp = 60.0d0 * (y / (t - z))
    else if (a <= 2.3d-41) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double tmp;
	if (a <= -7.4e-121) {
		tmp = a * 120.0;
	} else if (a <= -1.65e-289) {
		tmp = t_1;
	} else if (a <= 1.25e-235) {
		tmp = 60.0 * (y / (t - z));
	} else if (a <= 2.3e-41) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (x / (z - t))
	tmp = 0
	if a <= -7.4e-121:
		tmp = a * 120.0
	elif a <= -1.65e-289:
		tmp = t_1
	elif a <= 1.25e-235:
		tmp = 60.0 * (y / (t - z))
	elif a <= 2.3e-41:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(x / Float64(z - t)))
	tmp = 0.0
	if (a <= -7.4e-121)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.65e-289)
		tmp = t_1;
	elseif (a <= 1.25e-235)
		tmp = Float64(60.0 * Float64(y / Float64(t - z)));
	elseif (a <= 2.3e-41)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * (x / (z - t));
	tmp = 0.0;
	if (a <= -7.4e-121)
		tmp = a * 120.0;
	elseif (a <= -1.65e-289)
		tmp = t_1;
	elseif (a <= 1.25e-235)
		tmp = 60.0 * (y / (t - z));
	elseif (a <= 2.3e-41)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.4e-121], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.65e-289], t$95$1, If[LessEqual[a, 1.25e-235], N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e-41], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.4000000000000004e-121 or 2.3000000000000001e-41 < a

   1. Initial program 98.6%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 63.6%

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

   if -7.4000000000000004e-121 < a < -1.64999999999999999e-289 or 1.2499999999999999e-235 < a < 2.3000000000000001e-41

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 53.1%

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

   if -1.64999999999999999e-289 < a < 1.2499999999999999e-235

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 99.6%

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

      3. fma-define 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. neg-sub0 99.6%

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

      7. associate-+l- 99.6%

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

      8. sub0-neg 99.6%

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

      9. distribute-frac-neg2 99.6%

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

      10. distribute-neg-frac 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 72.0%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.4 \cdot 10^{-121}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-289}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-235}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-41}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-58} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-39}\right):\\ \;\;\;\;60 \cdot \frac{y}{t - z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -2e-58) (not (<= (* a 120.0) 5e-39)))
   (+ (* 60.0 (/ y (- t z))) (* a 120.0))
   (/ (- x y) (* (- z t) 0.016666666666666666))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2e-58) || !((a * 120.0) <= 5e-39)) {
		tmp = (60.0 * (y / (t - z))) + (a * 120.0);
	} else {
		tmp = (x - y) / ((z - t) * 0.016666666666666666);
	}
	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 (((a * 120.0d0) <= (-2d-58)) .or. (.not. ((a * 120.0d0) <= 5d-39))) then
        tmp = (60.0d0 * (y / (t - z))) + (a * 120.0d0)
    else
        tmp = (x - y) / ((z - t) * 0.016666666666666666d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2e-58) || !((a * 120.0) <= 5e-39)) {
		tmp = (60.0 * (y / (t - z))) + (a * 120.0);
	} else {
		tmp = (x - y) / ((z - t) * 0.016666666666666666);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -2e-58) or not ((a * 120.0) <= 5e-39):
		tmp = (60.0 * (y / (t - z))) + (a * 120.0)
	else:
		tmp = (x - y) / ((z - t) * 0.016666666666666666)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -2e-58) || !(Float64(a * 120.0) <= 5e-39))
		tmp = Float64(Float64(60.0 * Float64(y / Float64(t - z))) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(x - y) / Float64(Float64(z - t) * 0.016666666666666666));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -2e-58) || ~(((a * 120.0) <= 5e-39)))
		tmp = (60.0 * (y / (t - z))) + (a * 120.0);
	else
		tmp = (x - y) / ((z - t) * 0.016666666666666666);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-58], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-39]], $MachinePrecision]], N[(N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(N[(z - t), $MachinePrecision] * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -2.0000000000000001e-58 or 4.9999999999999998e-39 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.6%

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

      1. *-commutative 98.6%

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

      2. associate-/l* 99.2%

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

      3. fma-define 99.2%

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

      4. sub-neg 99.2%

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

      5. +-commutative 99.2%

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

      6. neg-sub0 99.2%

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

      7. associate-+l- 99.2%

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

      8. sub0-neg 99.2%

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

      9. distribute-frac-neg2 99.2%

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

      10. distribute-neg-frac 99.2%

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

      11. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around 0 82.9%

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

   if -2.0000000000000001e-58 < (*.f64 a #s(literal 120 binary64)) < 4.9999999999999998e-39

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 84.5%

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

      1. associate-*r/ 84.6%

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

      2. *-rgt-identity 84.6%

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

      3. times-frac 84.6%

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

      4. /-rgt-identity 84.6%

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

   7. Simplified 84.6%

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

      1. clear-num 84.5%

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

      2. inv-pow 84.5%

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

      3. div-inv 84.5%

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

      4. metadata-eval 84.5%

         \[\leadsto {\left(\left(z - t\right) \cdot \color{blue}{0.016666666666666666}\right)}^{-1} \cdot \left(x - y\right) \]

   9. Applied egg-rr 84.5%

      \[\leadsto \color{blue}{{\left(\left(z - t\right) \cdot 0.016666666666666666\right)}^{-1}} \cdot \left(x - y\right) \]
   10. Step-by-step derivation

       1. unpow-1 84.5%

          \[\leadsto \color{blue}{\frac{1}{\left(z - t\right) \cdot 0.016666666666666666}} \cdot \left(x - y\right) \]

   11. Simplified 84.5%

       \[\leadsto \color{blue}{\frac{1}{\left(z - t\right) \cdot 0.016666666666666666}} \cdot \left(x - y\right) \]
   12. Step-by-step derivation

       1. associate-*l/ 84.6%

          \[\leadsto \color{blue}{\frac{1 \cdot \left(x - y\right)}{\left(z - t\right) \cdot 0.016666666666666666}} \]

       2. *-un-lft-identity 84.6%

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

   13. Applied egg-rr 84.6%

       \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-58} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-39}\right):\\ \;\;\;\;60 \cdot \frac{y}{t - z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -10000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-41}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -10000.0)
   (* a 120.0)
   (if (<= (* a 120.0) 1e-41)
     (* (- x y) (/ 60.0 (- z t)))
     (+ (* a 120.0) (* -60.0 (/ x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -10000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-41) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = (a * 120.0) + (-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) :: tmp
    if ((a * 120.0d0) <= (-10000.0d0)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-41) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else
        tmp = (a * 120.0d0) + ((-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 tmp;
	if ((a * 120.0) <= -10000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-41) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -10000.0:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-41:
		tmp = (x - y) * (60.0 / (z - t))
	else:
		tmp = (a * 120.0) + (-60.0 * (x / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -10000.0)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-41)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -10000.0)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-41)
		tmp = (x - y) * (60.0 / (z - t));
	else
		tmp = (a * 120.0) + (-60.0 * (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -10000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-41], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1e4

   1. Initial program 98.5%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in z around inf 71.1%

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

   if -1e4 < (*.f64 a #s(literal 120 binary64)) < 1.00000000000000001e-41

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 82.2%

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

      1. associate-*r/ 82.3%

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

      2. *-rgt-identity 82.3%

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

      3. times-frac 82.2%

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

      4. /-rgt-identity 82.2%

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

   7. Simplified 82.2%

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

   if 1.00000000000000001e-41 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.3%

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

   3. Taylor expanded in x around inf 86.2%

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

   4. Taylor expanded in z around 0 70.8%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -10000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-41}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -10000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-41}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -10000.0)
   (* a 120.0)
   (if (<= (* a 120.0) 1e-41)
     (/ 60.0 (/ (- z t) (- x y)))
     (+ (* a 120.0) (* -60.0 (/ x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -10000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-41) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = (a * 120.0) + (-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) :: tmp
    if ((a * 120.0d0) <= (-10000.0d0)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-41) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else
        tmp = (a * 120.0d0) + ((-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 tmp;
	if ((a * 120.0) <= -10000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-41) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -10000.0:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-41:
		tmp = 60.0 / ((z - t) / (x - y))
	else:
		tmp = (a * 120.0) + (-60.0 * (x / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -10000.0)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-41)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -10000.0)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-41)
		tmp = 60.0 / ((z - t) / (x - y));
	else
		tmp = (a * 120.0) + (-60.0 * (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -10000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-41], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1e4

   1. Initial program 98.5%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in z around inf 71.1%

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

   if -1e4 < (*.f64 a #s(literal 120 binary64)) < 1.00000000000000001e-41

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 82.2%

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

      1. associate-*r/ 82.3%

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

      2. *-rgt-identity 82.3%

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

      3. times-frac 82.2%

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

      4. /-rgt-identity 82.2%

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

      5. associate-/r/ 82.3%

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

   7. Simplified 82.3%

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

   if 1.00000000000000001e-41 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.3%

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

   3. Taylor expanded in x around inf 86.2%

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

   4. Taylor expanded in z around 0 70.8%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -10000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-41}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-60}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-138}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-39}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.5e-60)
   (* a 120.0)
   (if (<= a -1.15e-138)
     (* (- x y) (/ 60.0 z))
     (if (<= a 1.5e-39) (* (- x y) (/ -60.0 t)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.5e-60) {
		tmp = a * 120.0;
	} else if (a <= -1.15e-138) {
		tmp = (x - y) * (60.0 / z);
	} else if (a <= 1.5e-39) {
		tmp = (x - y) * (-60.0 / t);
	} else {
		tmp = a * 120.0;
	}
	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) :: tmp
    if (a <= (-6.5d-60)) then
        tmp = a * 120.0d0
    else if (a <= (-1.15d-138)) then
        tmp = (x - y) * (60.0d0 / z)
    else if (a <= 1.5d-39) then
        tmp = (x - y) * ((-60.0d0) / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.5e-60) {
		tmp = a * 120.0;
	} else if (a <= -1.15e-138) {
		tmp = (x - y) * (60.0 / z);
	} else if (a <= 1.5e-39) {
		tmp = (x - y) * (-60.0 / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.5e-60:
		tmp = a * 120.0
	elif a <= -1.15e-138:
		tmp = (x - y) * (60.0 / z)
	elif a <= 1.5e-39:
		tmp = (x - y) * (-60.0 / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.5e-60)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.15e-138)
		tmp = Float64(Float64(x - y) * Float64(60.0 / z));
	elseif (a <= 1.5e-39)
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.5e-60)
		tmp = a * 120.0;
	elseif (a <= -1.15e-138)
		tmp = (x - y) * (60.0 / z);
	elseif (a <= 1.5e-39)
		tmp = (x - y) * (-60.0 / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.5e-60], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.15e-138], N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e-39], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.49999999999999995e-60 or 1.50000000000000014e-39 < a

   1. Initial program 98.6%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 65.4%

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

   if -6.49999999999999995e-60 < a < -1.14999999999999995e-138

   1. Initial program 99.4%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 74.0%

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

      1. associate-*r/ 73.8%

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

      2. *-rgt-identity 73.8%

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

      3. times-frac 74.0%

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

      4. /-rgt-identity 74.0%

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

   7. Simplified 74.0%

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

   8. Taylor expanded in z around inf 65.1%

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

   if -1.14999999999999995e-138 < a < 1.50000000000000014e-39

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 85.9%

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

      1. associate-*r/ 85.9%

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

      2. *-rgt-identity 85.9%

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

      3. times-frac 85.9%

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

      4. /-rgt-identity 85.9%

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

   7. Simplified 85.9%

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

   8. Taylor expanded in z around 0 52.9%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-60}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-138}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-39}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 89.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+133} \lor \neg \left(y \leq 5 \cdot 10^{+47}\right):\\ \;\;\;\;60 \cdot \frac{y}{t - z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot 60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3e+133) (not (<= y 5e+47)))
   (+ (* 60.0 (/ y (- t z))) (* a 120.0))
   (+ (* a 120.0) (/ (* x 60.0) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3e+133) || !(y <= 5e+47)) {
		tmp = (60.0 * (y / (t - z))) + (a * 120.0);
	} else {
		tmp = (a * 120.0) + ((x * 60.0) / (z - 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) :: tmp
    if ((y <= (-3d+133)) .or. (.not. (y <= 5d+47))) then
        tmp = (60.0d0 * (y / (t - z))) + (a * 120.0d0)
    else
        tmp = (a * 120.0d0) + ((x * 60.0d0) / (z - t))
    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 <= -3e+133) || !(y <= 5e+47)) {
		tmp = (60.0 * (y / (t - z))) + (a * 120.0);
	} else {
		tmp = (a * 120.0) + ((x * 60.0) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3e+133) or not (y <= 5e+47):
		tmp = (60.0 * (y / (t - z))) + (a * 120.0)
	else:
		tmp = (a * 120.0) + ((x * 60.0) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3e+133) || !(y <= 5e+47))
		tmp = Float64(Float64(60.0 * Float64(y / Float64(t - z))) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * 60.0) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3e+133) || ~((y <= 5e+47)))
		tmp = (60.0 * (y / (t - z))) + (a * 120.0);
	else
		tmp = (a * 120.0) + ((x * 60.0) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3e+133], N[Not[LessEqual[y, 5e+47]], $MachinePrecision]], N[(N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.00000000000000007e133 or 5.00000000000000022e47 < y

   1. Initial program 98.0%

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

      1. *-commutative 98.0%

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

      2. associate-/l* 98.7%

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

      3. fma-define 98.7%

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

      4. sub-neg 98.7%

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

      5. +-commutative 98.7%

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

      6. neg-sub0 98.7%

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

      7. associate-+l- 98.7%

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

      8. sub0-neg 98.7%

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

      9. distribute-frac-neg2 98.7%

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

      10. distribute-neg-frac 98.7%

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

      11. metadata-eval 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around 0 89.0%

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

   if -3.00000000000000007e133 < y < 5.00000000000000022e47

   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 93.0%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+133} \lor \neg \left(y \leq 5 \cdot 10^{+47}\right):\\ \;\;\;\;60 \cdot \frac{y}{t - z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot 60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-121} \lor \neg \left(a \leq 3 \cdot 10^{-32}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8e-121) (not (<= a 3e-32)))
   (* a 120.0)
   (* 60.0 (/ x (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8e-121) || !(a <= 3e-32)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (x / (z - 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) :: tmp
    if ((a <= (-8d-121)) .or. (.not. (a <= 3d-32))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * (x / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8e-121) || !(a <= 3e-32)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (x / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8e-121) or not (a <= 3e-32):
		tmp = a * 120.0
	else:
		tmp = 60.0 * (x / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8e-121) || !(a <= 3e-32))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -8e-121) || ~((a <= 3e-32)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * (x / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8e-121], N[Not[LessEqual[a, 3e-32]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.9999999999999998e-121 or 3e-32 < a

   1. Initial program 98.6%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 63.6%

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

   if -7.9999999999999998e-121 < a < 3e-32

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 47.6%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-121} \lor \neg \left(a \leq 3 \cdot 10^{-32}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{+58} \lor \neg \left(x \leq 6.4 \cdot 10^{+201}\right):\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -4.9e+58) (not (<= x 6.4e+201))) (* -60.0 (/ x t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.9e+58) || !(x <= 6.4e+201)) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	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) :: tmp
    if ((x <= (-4.9d+58)) .or. (.not. (x <= 6.4d+201))) then
        tmp = (-60.0d0) * (x / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.9e+58) || !(x <= 6.4e+201)) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -4.9e+58) or not (x <= 6.4e+201):
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -4.9e+58) || !(x <= 6.4e+201))
		tmp = Float64(-60.0 * Float64(x / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -4.9e+58) || ~((x <= 6.4e+201)))
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -4.9e+58], N[Not[LessEqual[x, 6.4e+201]], $MachinePrecision]], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.90000000000000018e58 or 6.3999999999999998e201 < x

   1. Initial program 98.6%

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

      1. *-commutative 98.6%

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

      2. associate-/l* 99.7%

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

      3. fma-define 99.7%

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

      4. sub-neg 99.7%

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

      5. +-commutative 99.7%

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

      6. neg-sub0 99.7%

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

      7. associate-+l- 99.7%

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

      8. sub0-neg 99.7%

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

      9. distribute-frac-neg2 99.7%

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

      10. distribute-neg-frac 99.7%

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

      11. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 64.2%

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

      1. associate-*r/ 63.1%

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

   7. Simplified 63.1%

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

   8. Taylor expanded in t around inf 36.6%

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

   if -4.90000000000000018e58 < x < 6.3999999999999998e201

   1. Initial program 99.2%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 54.5%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{+58} \lor \neg \left(x \leq 6.4 \cdot 10^{+201}\right):\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+194} \lor \neg \left(x \leq 3.9 \cdot 10^{+202}\right):\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -5.5e+194) (not (<= x 3.9e+202))) (* 60.0 (/ x z)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -5.5e+194) || !(x <= 3.9e+202)) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	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) :: tmp
    if ((x <= (-5.5d+194)) .or. (.not. (x <= 3.9d+202))) then
        tmp = 60.0d0 * (x / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -5.5e+194) || !(x <= 3.9e+202)) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -5.5e+194) or not (x <= 3.9e+202):
		tmp = 60.0 * (x / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -5.5e+194) || !(x <= 3.9e+202))
		tmp = Float64(60.0 * Float64(x / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -5.5e+194) || ~((x <= 3.9e+202)))
		tmp = 60.0 * (x / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -5.5e+194], N[Not[LessEqual[x, 3.9e+202]], $MachinePrecision]], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.4999999999999999e194 or 3.89999999999999983e202 < x

   1. Initial program 98.1%

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

      1. *-commutative 98.1%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. distribute-frac-neg2 99.8%

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

      10. distribute-neg-frac 99.8%

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

      11. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 70.7%

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

      1. associate-*r/ 69.1%

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

   7. Simplified 69.1%

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

   8. Taylor expanded in t around 0 51.3%

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

   if -5.4999999999999999e194 < x < 3.89999999999999983e202

   1. Initial program 99.3%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 51.6%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+194} \lor \neg \left(x \leq 3.9 \cdot 10^{+202}\right):\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+228} \lor \neg \left(y \leq 4.2 \cdot 10^{+100}\right):\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.8e+228) (not (<= y 4.2e+100))) (* 60.0 (/ y t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.8e+228) || !(y <= 4.2e+100)) {
		tmp = 60.0 * (y / t);
	} else {
		tmp = a * 120.0;
	}
	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) :: tmp
    if ((y <= (-5.8d+228)) .or. (.not. (y <= 4.2d+100))) then
        tmp = 60.0d0 * (y / t)
    else
        tmp = a * 120.0d0
    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 <= -5.8e+228) || !(y <= 4.2e+100)) {
		tmp = 60.0 * (y / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5.8e+228) or not (y <= 4.2e+100):
		tmp = 60.0 * (y / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5.8e+228) || !(y <= 4.2e+100))
		tmp = Float64(60.0 * Float64(y / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -5.8e+228) || ~((y <= 4.2e+100)))
		tmp = 60.0 * (y / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5.8e+228], N[Not[LessEqual[y, 4.2e+100]], $MachinePrecision]], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.80000000000000003e228 or 4.1999999999999997e100 < y

   1. Initial program 98.3%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in a around 0 80.1%

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

      1. associate-*r/ 80.1%

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

      2. *-rgt-identity 80.1%

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

      3. times-frac 79.9%

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

      4. /-rgt-identity 79.9%

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

   7. Simplified 79.9%

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

   8. Taylor expanded in z around 0 53.0%

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

   9. Taylor expanded in x around 0 47.7%

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

   if -5.80000000000000003e228 < y < 4.1999999999999997e100

   1. Initial program 99.3%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 53.9%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+228} \lor \neg \left(y \leq 4.2 \cdot 10^{+100}\right):\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+229}:\\ \;\;\;\;\frac{y \cdot 60}{t}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+100}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.35e+229)
   (/ (* y 60.0) t)
   (if (<= y 3.8e+100) (* a 120.0) (* 60.0 (/ y t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.35e+229) {
		tmp = (y * 60.0) / t;
	} else if (y <= 3.8e+100) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / 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) :: tmp
    if (y <= (-2.35d+229)) then
        tmp = (y * 60.0d0) / t
    else if (y <= 3.8d+100) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * (y / t)
    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 <= -2.35e+229) {
		tmp = (y * 60.0) / t;
	} else if (y <= 3.8e+100) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.35e+229:
		tmp = (y * 60.0) / t
	elif y <= 3.8e+100:
		tmp = a * 120.0
	else:
		tmp = 60.0 * (y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.35e+229)
		tmp = Float64(Float64(y * 60.0) / t);
	elseif (y <= 3.8e+100)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.35e+229)
		tmp = (y * 60.0) / t;
	elseif (y <= 3.8e+100)
		tmp = a * 120.0;
	else
		tmp = 60.0 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.35e+229], N[(N[(y * 60.0), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 3.8e+100], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.35e229

   1. Initial program 100.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 84.9%

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

      1. associate-*r/ 85.3%

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

      2. *-rgt-identity 85.3%

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

      3. times-frac 84.9%

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

      4. /-rgt-identity 84.9%

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

   7. Simplified 84.9%

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

   8. Taylor expanded in z around 0 74.1%

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

      1. associate-*l/ 74.3%

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

   10. Applied egg-rr 74.3%

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

   11. Taylor expanded in x around 0 67.5%

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

       1. associate-*r/ 67.7%

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

   13. Simplified 67.7%

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

   if -2.35e229 < y < 3.79999999999999963e100

   1. Initial program 99.3%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 53.9%

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

   if 3.79999999999999963e100 < y

   1. Initial program 97.8%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in a around 0 78.7%

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

      1. associate-*r/ 78.7%

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

      2. *-rgt-identity 78.7%

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

      3. times-frac 78.5%

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

      4. /-rgt-identity 78.5%

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

   7. Simplified 78.5%

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

   8. Taylor expanded in z around 0 47.0%

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

   9. Taylor expanded in x around 0 42.1%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+229}:\\ \;\;\;\;\frac{y \cdot 60}{t}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+100}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 99.8% accurate, 1.0× speedup

Math

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

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(60.0 * Float64(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[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.0%

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

   1. associate-/l* 99.3%

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

3. Simplified 99.3%

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

5. Final simplification 99.3%

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

Alternative 19: 51.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{+137}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 2.2e+137) (* a 120.0) (* -60.0 (/ y z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 2.2e+137) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / 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) :: tmp
    if (y <= 2.2d+137) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (y / z)
    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 <= 2.2e+137) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 2.2e+137:
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 2.2e+137)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 2.2e+137)
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 2.2e+137], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.20000000000000015e137

   1. Initial program 99.3%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 50.1%

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

   if 2.20000000000000015e137 < y

   1. Initial program 97.6%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in a around 0 81.6%

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

      1. associate-*r/ 81.6%

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

      2. *-rgt-identity 81.6%

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

      3. times-frac 81.4%

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

      4. /-rgt-identity 81.4%

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

   7. Simplified 81.4%

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

      1. clear-num 81.4%

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

      2. inv-pow 81.4%

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

      3. div-inv 81.4%

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

      4. metadata-eval 81.4%

         \[\leadsto {\left(\left(z - t\right) \cdot \color{blue}{0.016666666666666666}\right)}^{-1} \cdot \left(x - y\right) \]

   9. Applied egg-rr 81.4%

      \[\leadsto \color{blue}{{\left(\left(z - t\right) \cdot 0.016666666666666666\right)}^{-1}} \cdot \left(x - y\right) \]
   10. Step-by-step derivation

       1. unpow-1 81.4%

          \[\leadsto \color{blue}{\frac{1}{\left(z - t\right) \cdot 0.016666666666666666}} \cdot \left(x - y\right) \]

   11. Simplified 81.4%

       \[\leadsto \color{blue}{\frac{1}{\left(z - t\right) \cdot 0.016666666666666666}} \cdot \left(x - y\right) \]

   12. Taylor expanded in z around inf 46.9%

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

   13. Taylor expanded in x around 0 40.4%

       \[\leadsto \color{blue}{-60 \cdot \frac{y}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{+137}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 50.4% accurate, 4.3× 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 99.0%

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

   1. associate-/l* 99.3%

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

3. Simplified 99.3%

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

5. Taylor expanded in z around inf 44.5%

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

6. Final simplification 44.5%

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

Developer target: 99.8% accurate, 1.0× 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 2024076 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

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

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