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

Percentage Accurate: 99.4% → 99.8%

Time: 16.1s

Alternatives: 19

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   2. fma-def 99.1%

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

   3. associate-*l/ 99.8%

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

3. Simplified 99.8%

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

   1. associate-/r/ 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   2. fma-def 99.1%

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

   3. associate-*l/ 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 3: 58.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z}\\ t_2 := -60 \cdot \frac{x - y}{t}\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{-14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-141}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-216}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{-220}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-53}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) z))) (t_2 (* -60.0 (/ (- x y) t))))
   (if (<= a -3.9e-14)
     (* a 120.0)
     (if (<= a -1.12e-141)
       (* 60.0 (/ x (- z t)))
       (if (<= a -9.2e-216)
         t_2
         (if (<= a -7.4e-264)
           t_1
           (if (<= a 8.4e-220)
             t_2
             (if (<= a 1.45e-186)
               t_1
               (if (<= a 2.7e-53) t_2 (* a 120.0))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / z);
	double t_2 = -60.0 * ((x - y) / t);
	double tmp;
	if (a <= -3.9e-14) {
		tmp = a * 120.0;
	} else if (a <= -1.12e-141) {
		tmp = 60.0 * (x / (z - t));
	} else if (a <= -9.2e-216) {
		tmp = t_2;
	} else if (a <= -7.4e-264) {
		tmp = t_1;
	} else if (a <= 8.4e-220) {
		tmp = t_2;
	} else if (a <= 1.45e-186) {
		tmp = t_1;
	} else if (a <= 2.7e-53) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / z)
    t_2 = (-60.0d0) * ((x - y) / t)
    if (a <= (-3.9d-14)) then
        tmp = a * 120.0d0
    else if (a <= (-1.12d-141)) then
        tmp = 60.0d0 * (x / (z - t))
    else if (a <= (-9.2d-216)) then
        tmp = t_2
    else if (a <= (-7.4d-264)) then
        tmp = t_1
    else if (a <= 8.4d-220) then
        tmp = t_2
    else if (a <= 1.45d-186) then
        tmp = t_1
    else if (a <= 2.7d-53) then
        tmp = t_2
    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 - y) / z);
	double t_2 = -60.0 * ((x - y) / t);
	double tmp;
	if (a <= -3.9e-14) {
		tmp = a * 120.0;
	} else if (a <= -1.12e-141) {
		tmp = 60.0 * (x / (z - t));
	} else if (a <= -9.2e-216) {
		tmp = t_2;
	} else if (a <= -7.4e-264) {
		tmp = t_1;
	} else if (a <= 8.4e-220) {
		tmp = t_2;
	} else if (a <= 1.45e-186) {
		tmp = t_1;
	} else if (a <= 2.7e-53) {
		tmp = t_2;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / z)
	t_2 = -60.0 * ((x - y) / t)
	tmp = 0
	if a <= -3.9e-14:
		tmp = a * 120.0
	elif a <= -1.12e-141:
		tmp = 60.0 * (x / (z - t))
	elif a <= -9.2e-216:
		tmp = t_2
	elif a <= -7.4e-264:
		tmp = t_1
	elif a <= 8.4e-220:
		tmp = t_2
	elif a <= 1.45e-186:
		tmp = t_1
	elif a <= 2.7e-53:
		tmp = t_2
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / z))
	t_2 = Float64(-60.0 * Float64(Float64(x - y) / t))
	tmp = 0.0
	if (a <= -3.9e-14)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.12e-141)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	elseif (a <= -9.2e-216)
		tmp = t_2;
	elseif (a <= -7.4e-264)
		tmp = t_1;
	elseif (a <= 8.4e-220)
		tmp = t_2;
	elseif (a <= 1.45e-186)
		tmp = t_1;
	elseif (a <= 2.7e-53)
		tmp = t_2;
	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 - y) / z);
	t_2 = -60.0 * ((x - y) / t);
	tmp = 0.0;
	if (a <= -3.9e-14)
		tmp = a * 120.0;
	elseif (a <= -1.12e-141)
		tmp = 60.0 * (x / (z - t));
	elseif (a <= -9.2e-216)
		tmp = t_2;
	elseif (a <= -7.4e-264)
		tmp = t_1;
	elseif (a <= 8.4e-220)
		tmp = t_2;
	elseif (a <= 1.45e-186)
		tmp = t_1;
	elseif (a <= 2.7e-53)
		tmp = t_2;
	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[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.9e-14], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.12e-141], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.2e-216], t$95$2, If[LessEqual[a, -7.4e-264], t$95$1, If[LessEqual[a, 8.4e-220], t$95$2, If[LessEqual[a, 1.45e-186], t$95$1, If[LessEqual[a, 2.7e-53], t$95$2, N[(a * 120.0), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.8999999999999998e-14 or 2.6999999999999999e-53 < a

   1. Initial program 99.2%

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

   2. Taylor expanded in z around inf 73.8%

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

   if -3.8999999999999998e-14 < a < -1.12000000000000002e-141

   1. Initial program 96.7%

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

      1. *-commutative 96.7%

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

      2. associate-/l* 99.8%

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

      3. frac-2neg 99.8%

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

      4. distribute-frac-neg 99.8%

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

      5. div-inv 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. metadata-eval 99.9%

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

      8. metadata-eval 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. +-commutative 99.9%

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

      2. unsub-neg 99.9%

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

      3. div-inv 99.7%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 99.7%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.7%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 56.9%

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

   if -1.12000000000000002e-141 < a < -9.19999999999999987e-216 or -7.39999999999999991e-264 < a < 8.3999999999999997e-220 or 1.4500000000000001e-186 < a < 2.6999999999999999e-53

   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%

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

      2. fma-def 99.7%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around 0 87.1%

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

   7. Taylor expanded in z around 0 62.6%

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

   if -9.19999999999999987e-216 < a < -7.39999999999999991e-264 or 8.3999999999999997e-220 < a < 1.4500000000000001e-186

   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%

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

      2. fma-def 99.6%

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

      3. associate-*l/ 99.5%

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

   3. Simplified 99.5%

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

      1. associate-/r/ 99.5%

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

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in a around 0 90.9%

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

   7. Taylor expanded in z around inf 72.5%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-141}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-216}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-264}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{-220}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-186}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-53}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 4: 82.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-10} \lor \neg \left(a \cdot 120 \leq 4 \cdot 10^{-50}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -5e-10) (not (<= (* a 120.0) 4e-50)))
   (+ (* -60.0 (/ y (- z t))) (* 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 * 120.0) <= -5e-10) || !((a * 120.0) <= 4e-50)) {
		tmp = (-60.0 * (y / (z - t))) + (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 * 120.0d0) <= (-5d-10)) .or. (.not. ((a * 120.0d0) <= 4d-50))) then
        tmp = ((-60.0d0) * (y / (z - t))) + (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 * 120.0) <= -5e-10) || !((a * 120.0) <= 4e-50)) {
		tmp = (-60.0 * (y / (z - t))) + (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 * 120.0) <= -5e-10) or not ((a * 120.0) <= 4e-50):
		tmp = (-60.0 * (y / (z - t))) + (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 ((Float64(a * 120.0) <= -5e-10) || !(Float64(a * 120.0) <= 4e-50))
		tmp = Float64(Float64(-60.0 * Float64(y / Float64(z - t))) + 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 * 120.0) <= -5e-10) || ~(((a * 120.0) <= 4e-50)))
		tmp = (-60.0 * (y / (z - t))) + (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[N[(a * 120.0), $MachinePrecision], -5e-10], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 4e-50]], $MachinePrecision]], N[(N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 120) < -5.00000000000000031e-10 or 4.00000000000000003e-50 < (*.f64 a 120)

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0 87.2%

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

   if -5.00000000000000031e-10 < (*.f64 a 120) < 4.00000000000000003e-50

   1. Initial program 98.8%

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

      1. +-commutative 98.8%

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

      2. fma-def 98.8%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around 0 83.9%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-10} \lor \neg \left(a \cdot 120 \leq 4 \cdot 10^{-50}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 5: 58.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x - y}{t}\\ t_2 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{-14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-259}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ (- x y) t))) (t_2 (* 60.0 (/ x (- z t)))))
   (if (<= a -3.4e-14)
     (* a 120.0)
     (if (<= a -1.4e-141)
       t_2
       (if (<= a 6.5e-259)
         t_1
         (if (<= a 1.5e-169) t_2 (if (<= a 2.1e-58) t_1 (* a 120.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * ((x - y) / t);
	double t_2 = 60.0 * (x / (z - t));
	double tmp;
	if (a <= -3.4e-14) {
		tmp = a * 120.0;
	} else if (a <= -1.4e-141) {
		tmp = t_2;
	} else if (a <= 6.5e-259) {
		tmp = t_1;
	} else if (a <= 1.5e-169) {
		tmp = t_2;
	} else if (a <= 2.1e-58) {
		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) :: t_2
    real(8) :: tmp
    t_1 = (-60.0d0) * ((x - y) / t)
    t_2 = 60.0d0 * (x / (z - t))
    if (a <= (-3.4d-14)) then
        tmp = a * 120.0d0
    else if (a <= (-1.4d-141)) then
        tmp = t_2
    else if (a <= 6.5d-259) then
        tmp = t_1
    else if (a <= 1.5d-169) then
        tmp = t_2
    else if (a <= 2.1d-58) 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 - y) / t);
	double t_2 = 60.0 * (x / (z - t));
	double tmp;
	if (a <= -3.4e-14) {
		tmp = a * 120.0;
	} else if (a <= -1.4e-141) {
		tmp = t_2;
	} else if (a <= 6.5e-259) {
		tmp = t_1;
	} else if (a <= 1.5e-169) {
		tmp = t_2;
	} else if (a <= 2.1e-58) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * ((x - y) / t)
	t_2 = 60.0 * (x / (z - t))
	tmp = 0
	if a <= -3.4e-14:
		tmp = a * 120.0
	elif a <= -1.4e-141:
		tmp = t_2
	elif a <= 6.5e-259:
		tmp = t_1
	elif a <= 1.5e-169:
		tmp = t_2
	elif a <= 2.1e-58:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(Float64(x - y) / t))
	t_2 = Float64(60.0 * Float64(x / Float64(z - t)))
	tmp = 0.0
	if (a <= -3.4e-14)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.4e-141)
		tmp = t_2;
	elseif (a <= 6.5e-259)
		tmp = t_1;
	elseif (a <= 1.5e-169)
		tmp = t_2;
	elseif (a <= 2.1e-58)
		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 - y) / t);
	t_2 = 60.0 * (x / (z - t));
	tmp = 0.0;
	if (a <= -3.4e-14)
		tmp = a * 120.0;
	elseif (a <= -1.4e-141)
		tmp = t_2;
	elseif (a <= 6.5e-259)
		tmp = t_1;
	elseif (a <= 1.5e-169)
		tmp = t_2;
	elseif (a <= 2.1e-58)
		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[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e-14], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.4e-141], t$95$2, If[LessEqual[a, 6.5e-259], t$95$1, If[LessEqual[a, 1.5e-169], t$95$2, If[LessEqual[a, 2.1e-58], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.40000000000000003e-14 or 2.09999999999999988e-58 < a

   1. Initial program 99.2%

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

   2. Taylor expanded in z around inf 73.8%

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

   if -3.40000000000000003e-14 < a < -1.40000000000000006e-141 or 6.50000000000000045e-259 < a < 1.5e-169

   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* 99.6%

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

      3. frac-2neg 99.6%

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

      4. distribute-frac-neg 99.6%

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

      5. div-inv 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. metadata-eval 99.7%

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

      8. metadata-eval 99.7%

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

   3. Applied egg-rr 99.7%

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

      1. +-commutative 99.7%

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

      2. unsub-neg 99.7%

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

      3. div-inv 99.5%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 99.5%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.6%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in x around inf 54.4%

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

   if -1.40000000000000006e-141 < a < 6.50000000000000045e-259 or 1.5e-169 < a < 2.09999999999999988e-58

   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%

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

      2. fma-def 99.7%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.5%

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

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in a around 0 88.6%

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

   7. Taylor expanded in z around 0 55.9%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-141}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-259}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-169}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-58}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 6: 58.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -1.14 \cdot 10^{-13}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.15 \cdot 10^{-201}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-55}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ x (- z t)))))
   (if (<= a -1.14e-13)
     (* a 120.0)
     (if (<= a -1.75e-149)
       t_1
       (if (<= a 3.15e-201)
         (* y (/ -60.0 (- z t)))
         (if (<= a 4e-150)
           t_1
           (if (<= a 1.6e-55) (* -60.0 (/ (- x y) t)) (* 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 <= -1.14e-13) {
		tmp = a * 120.0;
	} else if (a <= -1.75e-149) {
		tmp = t_1;
	} else if (a <= 3.15e-201) {
		tmp = y * (-60.0 / (z - t));
	} else if (a <= 4e-150) {
		tmp = t_1;
	} else if (a <= 1.6e-55) {
		tmp = -60.0 * ((x - 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) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * (x / (z - t))
    if (a <= (-1.14d-13)) then
        tmp = a * 120.0d0
    else if (a <= (-1.75d-149)) then
        tmp = t_1
    else if (a <= 3.15d-201) then
        tmp = y * ((-60.0d0) / (z - t))
    else if (a <= 4d-150) then
        tmp = t_1
    else if (a <= 1.6d-55) then
        tmp = (-60.0d0) * ((x - 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 t_1 = 60.0 * (x / (z - t));
	double tmp;
	if (a <= -1.14e-13) {
		tmp = a * 120.0;
	} else if (a <= -1.75e-149) {
		tmp = t_1;
	} else if (a <= 3.15e-201) {
		tmp = y * (-60.0 / (z - t));
	} else if (a <= 4e-150) {
		tmp = t_1;
	} else if (a <= 1.6e-55) {
		tmp = -60.0 * ((x - y) / t);
	} 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 <= -1.14e-13:
		tmp = a * 120.0
	elif a <= -1.75e-149:
		tmp = t_1
	elif a <= 3.15e-201:
		tmp = y * (-60.0 / (z - t))
	elif a <= 4e-150:
		tmp = t_1
	elif a <= 1.6e-55:
		tmp = -60.0 * ((x - y) / t)
	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 <= -1.14e-13)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.75e-149)
		tmp = t_1;
	elseif (a <= 3.15e-201)
		tmp = Float64(y * Float64(-60.0 / Float64(z - t)));
	elseif (a <= 4e-150)
		tmp = t_1;
	elseif (a <= 1.6e-55)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	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 <= -1.14e-13)
		tmp = a * 120.0;
	elseif (a <= -1.75e-149)
		tmp = t_1;
	elseif (a <= 3.15e-201)
		tmp = y * (-60.0 / (z - t));
	elseif (a <= 4e-150)
		tmp = t_1;
	elseif (a <= 1.6e-55)
		tmp = -60.0 * ((x - y) / t);
	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, -1.14e-13], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.75e-149], t$95$1, If[LessEqual[a, 3.15e-201], N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e-150], t$95$1, If[LessEqual[a, 1.6e-55], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.13999999999999994e-13 or 1.6000000000000001e-55 < a

   1. Initial program 99.2%

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

   2. Taylor expanded in z around inf 73.8%

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

   if -1.13999999999999994e-13 < a < -1.75e-149 or 3.15e-201 < a < 4.00000000000000003e-150

   1. Initial program 97.7%

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

      1. *-commutative 97.7%

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

      2. associate-/l* 99.7%

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

      3. frac-2neg 99.7%

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

      4. distribute-frac-neg 99.7%

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

      5. div-inv 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. metadata-eval 99.7%

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

      8. metadata-eval 99.7%

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

   3. Applied egg-rr 99.7%

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

      1. +-commutative 99.7%

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

      2. unsub-neg 99.7%

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

      3. div-inv 99.6%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 99.6%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.7%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 58.7%

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

   if -1.75e-149 < a < 3.15e-201

   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%

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

      3. frac-2neg 99.6%

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

      4. distribute-frac-neg 99.6%

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

      5. div-inv 99.6%

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

      6. distribute-rgt-neg-in 99.6%

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

      7. metadata-eval 99.6%

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

      8. metadata-eval 99.6%

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

   3. Applied egg-rr 99.6%

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

      1. +-commutative 99.6%

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

      2. unsub-neg 99.6%

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

      3. div-inv 99.5%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 99.5%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.5%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.5%

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

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in x around 0 70.2%

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

      1. associate-*r/ 70.3%

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

   8. Simplified 70.3%

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

   9. Taylor expanded in a around 0 58.6%

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

       1. associate-*r/ 58.7%

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

       2. associate-*l/ 58.6%

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

       3. *-commutative 58.6%

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

   11. Simplified 58.6%

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

   if 4.00000000000000003e-150 < a < 1.6000000000000001e-55

   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%

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

      2. fma-def 99.7%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around 0 91.5%

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

   7. Taylor expanded in z around 0 67.2%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.14 \cdot 10^{-13}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-149}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 3.15 \cdot 10^{-201}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-150}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-55}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7: 58.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-147}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-201}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-110}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-53}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.9e-14)
   (* a 120.0)
   (if (<= a -1.45e-147)
     (* 60.0 (/ x (- z t)))
     (if (<= a 4.2e-201)
       (* y (/ -60.0 (- z t)))
       (if (<= a 9e-110)
         (/ 60.0 (/ (- z t) x))
         (if (<= a 1.7e-53) (* -60.0 (/ (- x y) t)) (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.9e-14) {
		tmp = a * 120.0;
	} else if (a <= -1.45e-147) {
		tmp = 60.0 * (x / (z - t));
	} else if (a <= 4.2e-201) {
		tmp = y * (-60.0 / (z - t));
	} else if (a <= 9e-110) {
		tmp = 60.0 / ((z - t) / x);
	} else if (a <= 1.7e-53) {
		tmp = -60.0 * ((x - 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 (a <= (-2.9d-14)) then
        tmp = a * 120.0d0
    else if (a <= (-1.45d-147)) then
        tmp = 60.0d0 * (x / (z - t))
    else if (a <= 4.2d-201) then
        tmp = y * ((-60.0d0) / (z - t))
    else if (a <= 9d-110) then
        tmp = 60.0d0 / ((z - t) / x)
    else if (a <= 1.7d-53) then
        tmp = (-60.0d0) * ((x - 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 (a <= -2.9e-14) {
		tmp = a * 120.0;
	} else if (a <= -1.45e-147) {
		tmp = 60.0 * (x / (z - t));
	} else if (a <= 4.2e-201) {
		tmp = y * (-60.0 / (z - t));
	} else if (a <= 9e-110) {
		tmp = 60.0 / ((z - t) / x);
	} else if (a <= 1.7e-53) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.9e-14:
		tmp = a * 120.0
	elif a <= -1.45e-147:
		tmp = 60.0 * (x / (z - t))
	elif a <= 4.2e-201:
		tmp = y * (-60.0 / (z - t))
	elif a <= 9e-110:
		tmp = 60.0 / ((z - t) / x)
	elif a <= 1.7e-53:
		tmp = -60.0 * ((x - y) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.9e-14)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.45e-147)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	elseif (a <= 4.2e-201)
		tmp = Float64(y * Float64(-60.0 / Float64(z - t)));
	elseif (a <= 9e-110)
		tmp = Float64(60.0 / Float64(Float64(z - t) / x));
	elseif (a <= 1.7e-53)
		tmp = Float64(-60.0 * Float64(Float64(x - 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 (a <= -2.9e-14)
		tmp = a * 120.0;
	elseif (a <= -1.45e-147)
		tmp = 60.0 * (x / (z - t));
	elseif (a <= 4.2e-201)
		tmp = y * (-60.0 / (z - t));
	elseif (a <= 9e-110)
		tmp = 60.0 / ((z - t) / x);
	elseif (a <= 1.7e-53)
		tmp = -60.0 * ((x - y) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.9e-14], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.45e-147], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e-201], N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e-110], N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e-53], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.9000000000000003e-14 or 1.7e-53 < a

   1. Initial program 99.2%

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

   2. Taylor expanded in z around inf 73.8%

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

   if -2.9000000000000003e-14 < a < -1.4500000000000001e-147

   1. Initial program 96.8%

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

      1. *-commutative 96.8%

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

      2. associate-/l* 99.8%

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

      3. frac-2neg 99.8%

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

      4. distribute-frac-neg 99.8%

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

      5. div-inv 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. metadata-eval 99.9%

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

      8. metadata-eval 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. +-commutative 99.9%

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

      2. unsub-neg 99.9%

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

      3. div-inv 99.6%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 99.6%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.7%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 58.2%

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

   if -1.4500000000000001e-147 < a < 4.20000000000000024e-201

   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%

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

      3. frac-2neg 99.6%

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

      4. distribute-frac-neg 99.6%

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

      5. div-inv 99.6%

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

      6. distribute-rgt-neg-in 99.6%

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

      7. metadata-eval 99.6%

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

      8. metadata-eval 99.6%

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

   3. Applied egg-rr 99.6%

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

      1. +-commutative 99.6%

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

      2. unsub-neg 99.6%

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

      3. div-inv 99.5%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 99.5%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.5%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.5%

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

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in x around 0 70.2%

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

      1. associate-*r/ 70.3%

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

   8. Simplified 70.3%

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

   9. Taylor expanded in a around 0 58.6%

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

       1. associate-*r/ 58.7%

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

       2. associate-*l/ 58.6%

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

       3. *-commutative 58.6%

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

   11. Simplified 58.6%

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

   if 4.20000000000000024e-201 < a < 9.0000000000000002e-110

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.4%

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

      3. frac-2neg 99.4%

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

      4. distribute-frac-neg 99.4%

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

      5. div-inv 99.4%

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

      6. distribute-rgt-neg-in 99.4%

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

      7. metadata-eval 99.4%

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

      8. metadata-eval 99.4%

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

   3. Applied egg-rr 99.4%

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

      1. +-commutative 99.4%

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

      2. unsub-neg 99.4%

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

      3. div-inv 99.5%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 99.5%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.5%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.5%

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

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in x around inf 54.1%

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

      1. associate-*r/ 54.2%

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

      2. associate-/l* 54.3%

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

   8. Applied egg-rr 54.3%

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

   if 9.0000000000000002e-110 < a < 1.7e-53

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-def 99.7%

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

      3. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.4%

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

   5. Applied egg-rr 99.4%

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

   6. Taylor expanded in a around 0 100.0%

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

   7. Taylor expanded in z around 0 100.0%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-147}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-201}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-110}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-53}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 8: 58.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-144}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-201}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-109}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-55}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.4e-14)
   (* a 120.0)
   (if (<= a -7.4e-144)
     (* 60.0 (/ x (- z t)))
     (if (<= a 4.7e-201)
       (/ (* y -60.0) (- z t))
       (if (<= a 1.8e-109)
         (/ 60.0 (/ (- z t) x))
         (if (<= a 6.5e-55) (* -60.0 (/ (- x y) t)) (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.4e-14) {
		tmp = a * 120.0;
	} else if (a <= -7.4e-144) {
		tmp = 60.0 * (x / (z - t));
	} else if (a <= 4.7e-201) {
		tmp = (y * -60.0) / (z - t);
	} else if (a <= 1.8e-109) {
		tmp = 60.0 / ((z - t) / x);
	} else if (a <= 6.5e-55) {
		tmp = -60.0 * ((x - 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 (a <= (-2.4d-14)) then
        tmp = a * 120.0d0
    else if (a <= (-7.4d-144)) then
        tmp = 60.0d0 * (x / (z - t))
    else if (a <= 4.7d-201) then
        tmp = (y * (-60.0d0)) / (z - t)
    else if (a <= 1.8d-109) then
        tmp = 60.0d0 / ((z - t) / x)
    else if (a <= 6.5d-55) then
        tmp = (-60.0d0) * ((x - 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 (a <= -2.4e-14) {
		tmp = a * 120.0;
	} else if (a <= -7.4e-144) {
		tmp = 60.0 * (x / (z - t));
	} else if (a <= 4.7e-201) {
		tmp = (y * -60.0) / (z - t);
	} else if (a <= 1.8e-109) {
		tmp = 60.0 / ((z - t) / x);
	} else if (a <= 6.5e-55) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.4e-14:
		tmp = a * 120.0
	elif a <= -7.4e-144:
		tmp = 60.0 * (x / (z - t))
	elif a <= 4.7e-201:
		tmp = (y * -60.0) / (z - t)
	elif a <= 1.8e-109:
		tmp = 60.0 / ((z - t) / x)
	elif a <= 6.5e-55:
		tmp = -60.0 * ((x - y) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.4e-14)
		tmp = Float64(a * 120.0);
	elseif (a <= -7.4e-144)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	elseif (a <= 4.7e-201)
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	elseif (a <= 1.8e-109)
		tmp = Float64(60.0 / Float64(Float64(z - t) / x));
	elseif (a <= 6.5e-55)
		tmp = Float64(-60.0 * Float64(Float64(x - 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 (a <= -2.4e-14)
		tmp = a * 120.0;
	elseif (a <= -7.4e-144)
		tmp = 60.0 * (x / (z - t));
	elseif (a <= 4.7e-201)
		tmp = (y * -60.0) / (z - t);
	elseif (a <= 1.8e-109)
		tmp = 60.0 / ((z - t) / x);
	elseif (a <= 6.5e-55)
		tmp = -60.0 * ((x - y) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.4e-14], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -7.4e-144], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.7e-201], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e-109], N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-55], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.4e-14 or 6.50000000000000006e-55 < a

   1. Initial program 99.2%

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

   2. Taylor expanded in z around inf 73.8%

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

   if -2.4e-14 < a < -7.4000000000000005e-144

   1. Initial program 96.8%

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

      1. *-commutative 96.8%

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

      2. associate-/l* 99.8%

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

      3. frac-2neg 99.8%

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

      4. distribute-frac-neg 99.8%

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

      5. div-inv 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. metadata-eval 99.9%

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

      8. metadata-eval 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. +-commutative 99.9%

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

      2. unsub-neg 99.9%

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

      3. div-inv 99.6%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 99.6%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.7%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 58.2%

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

   if -7.4000000000000005e-144 < a < 4.69999999999999994e-201

   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%

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

      3. frac-2neg 99.6%

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

      4. distribute-frac-neg 99.6%

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

      5. div-inv 99.6%

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

      6. distribute-rgt-neg-in 99.6%

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

      7. metadata-eval 99.6%

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

      8. metadata-eval 99.6%

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

   3. Applied egg-rr 99.6%

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

      1. +-commutative 99.6%

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

      2. unsub-neg 99.6%

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

      3. div-inv 99.5%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 99.5%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.5%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.5%

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

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in y around inf 58.6%

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

      1. associate-*r/ 58.7%

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

   8. Simplified 58.7%

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

   if 4.69999999999999994e-201 < a < 1.8e-109

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.4%

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

      3. frac-2neg 99.4%

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

      4. distribute-frac-neg 99.4%

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

      5. div-inv 99.4%

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

      6. distribute-rgt-neg-in 99.4%

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

      7. metadata-eval 99.4%

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

      8. metadata-eval 99.4%

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

   3. Applied egg-rr 99.4%

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

      1. +-commutative 99.4%

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

      2. unsub-neg 99.4%

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

      3. div-inv 99.5%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 99.5%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.5%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.5%

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

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in x around inf 54.1%

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

      1. associate-*r/ 54.2%

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

      2. associate-/l* 54.3%

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

   8. Applied egg-rr 54.3%

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

   if 1.8e-109 < a < 6.50000000000000006e-55

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-def 99.7%

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

      3. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.4%

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

   5. Applied egg-rr 99.4%

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

   6. Taylor expanded in a around 0 100.0%

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

   7. Taylor expanded in z around 0 100.0%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-14}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-144}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-201}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-109}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-55}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9: 74.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-10} \lor \neg \left(a \cdot 120 \leq 4 \cdot 10^{-50}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -5e-10) (not (<= (* a 120.0) 4e-50)))
   (* 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 * 120.0) <= -5e-10) || !((a * 120.0) <= 4e-50)) {
		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 * 120.0d0) <= (-5d-10)) .or. (.not. ((a * 120.0d0) <= 4d-50))) 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 * 120.0) <= -5e-10) || !((a * 120.0) <= 4e-50)) {
		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 * 120.0) <= -5e-10) or not ((a * 120.0) <= 4e-50):
		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 ((Float64(a * 120.0) <= -5e-10) || !(Float64(a * 120.0) <= 4e-50))
		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 * 120.0) <= -5e-10) || ~(((a * 120.0) <= 4e-50)))
		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[N[(a * 120.0), $MachinePrecision], -5e-10], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 4e-50]], $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 (*.f64 a 120) < -5.00000000000000031e-10 or 4.00000000000000003e-50 < (*.f64 a 120)

   1. Initial program 99.2%

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

   2. Taylor expanded in z around inf 74.1%

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

   if -5.00000000000000031e-10 < (*.f64 a 120) < 4.00000000000000003e-50

   1. Initial program 98.8%

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

      1. +-commutative 98.8%

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

      2. fma-def 98.8%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around 0 83.9%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-10} \lor \neg \left(a \cdot 120 \leq 4 \cdot 10^{-50}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 10: 72.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-10} \lor \neg \left(a \cdot 120 \leq 4 \cdot 10^{-50}\right):\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -5e-10) (not (<= (* a 120.0) 4e-50)))
   (+ (* a 120.0) (/ (* x -60.0) t))
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -5e-10) || !((a * 120.0) <= 4e-50)) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} 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 * 120.0d0) <= (-5d-10)) .or. (.not. ((a * 120.0d0) <= 4d-50))) then
        tmp = (a * 120.0d0) + ((x * (-60.0d0)) / t)
    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 * 120.0) <= -5e-10) || !((a * 120.0) <= 4e-50)) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -5e-10) or not ((a * 120.0) <= 4e-50):
		tmp = (a * 120.0) + ((x * -60.0) / t)
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -5e-10) || !(Float64(a * 120.0) <= 4e-50))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * -60.0) / t));
	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 * 120.0) <= -5e-10) || ~(((a * 120.0) <= 4e-50)))
		tmp = (a * 120.0) + ((x * -60.0) / t);
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-10], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 4e-50]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 120) < -5.00000000000000031e-10 or 4.00000000000000003e-50 < (*.f64 a 120)

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf 87.4%

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

   3. Taylor expanded in z around 0 75.5%

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

      1. associate-*r/ 12.4%

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

   5. Simplified 75.5%

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

   if -5.00000000000000031e-10 < (*.f64 a 120) < 4.00000000000000003e-50

   1. Initial program 98.8%

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

      1. +-commutative 98.8%

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

      2. fma-def 98.8%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around 0 83.9%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-10} \lor \neg \left(a \cdot 120 \leq 4 \cdot 10^{-50}\right):\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 11: 72.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-10}:\\ \;\;\;\;a \cdot 120 - -60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-50}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -5e-10)
   (- (* a 120.0) (* -60.0 (/ y t)))
   (if (<= (* a 120.0) 4e-50)
     (* 60.0 (/ (- x y) (- z t)))
     (+ (* a 120.0) (/ (* x -60.0) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e-10) {
		tmp = (a * 120.0) - (-60.0 * (y / t));
	} else if ((a * 120.0) <= 4e-50) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-5d-10)) then
        tmp = (a * 120.0d0) - ((-60.0d0) * (y / t))
    else if ((a * 120.0d0) <= 4d-50) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (a * 120.0d0) + ((x * (-60.0d0)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e-10) {
		tmp = (a * 120.0) - (-60.0 * (y / t));
	} else if ((a * 120.0) <= 4e-50) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -5e-10:
		tmp = (a * 120.0) - (-60.0 * (y / t))
	elif (a * 120.0) <= 4e-50:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (a * 120.0) + ((x * -60.0) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e-10)
		tmp = Float64(Float64(a * 120.0) - Float64(-60.0 * Float64(y / t)));
	elseif (Float64(a * 120.0) <= 4e-50)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * -60.0) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -5e-10)
		tmp = (a * 120.0) - (-60.0 * (y / t));
	elseif ((a * 120.0) <= 4e-50)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (a * 120.0) + ((x * -60.0) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-10], N[(N[(a * 120.0), $MachinePrecision] - N[(-60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 4e-50], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -5.00000000000000031e-10

   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* 99.9%

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

      3. frac-2neg 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. div-inv 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. metadata-eval 99.9%

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

      8. metadata-eval 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in z around 0 79.1%

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

      1. *-commutative 79.1%

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

   6. Simplified 79.1%

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

   7. Taylor expanded in x around 0 78.9%

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

   if -5.00000000000000031e-10 < (*.f64 a 120) < 4.00000000000000003e-50

   1. Initial program 98.8%

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

      1. +-commutative 98.8%

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

      2. fma-def 98.8%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around 0 83.9%

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

   if 4.00000000000000003e-50 < (*.f64 a 120)

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 93.4%

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

   3. Taylor expanded in z around 0 77.1%

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

      1. associate-*r/ 14.7%

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

   5. Simplified 77.1%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-10}:\\ \;\;\;\;a \cdot 120 - -60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-50}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \end{array} \]

Alternative 12: 89.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-35} \lor \neg \left(x \leq 1.12 \cdot 10^{+101}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -9e-35) (not (<= x 1.12e+101)))
   (+ (* 60.0 (/ x (- z t))) (* a 120.0))
   (+ (* -60.0 (/ y (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -9e-35) || !(x <= 1.12e+101)) {
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	} else {
		tmp = (-60.0 * (y / (z - t))) + (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 <= (-9d-35)) .or. (.not. (x <= 1.12d+101))) then
        tmp = (60.0d0 * (x / (z - t))) + (a * 120.0d0)
    else
        tmp = ((-60.0d0) * (y / (z - t))) + (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 <= -9e-35) || !(x <= 1.12e+101)) {
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	} else {
		tmp = (-60.0 * (y / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -9e-35) or not (x <= 1.12e+101):
		tmp = (60.0 * (x / (z - t))) + (a * 120.0)
	else:
		tmp = (-60.0 * (y / (z - t))) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -9e-35) || !(x <= 1.12e+101))
		tmp = Float64(Float64(60.0 * Float64(x / Float64(z - t))) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(-60.0 * Float64(y / Float64(z - t))) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -9e-35) || ~((x <= 1.12e+101)))
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	else
		tmp = (-60.0 * (y / (z - t))) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -9e-35], N[Not[LessEqual[x, 1.12e+101]], $MachinePrecision]], N[(N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.0000000000000002e-35 or 1.1199999999999999e101 < x

   1. Initial program 99.0%

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

   2. Taylor expanded in x around inf 91.5%

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

   if -9.0000000000000002e-35 < x < 1.1199999999999999e101

   1. Initial program 99.1%

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

   2. Taylor expanded in x around 0 92.6%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-35} \lor \neg \left(x \leq 1.12 \cdot 10^{+101}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t} + a \cdot 120\\ \end{array} \]

Alternative 13: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return ((x - y) * (60.0 / (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 = ((x - y) * (60.0d0 / (z - t))) + (a * 120.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x - y), $MachinePrecision] * N[(60.0 / 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/ 99.7%

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

3. Applied egg-rr 99.7%

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

4. Final simplification 99.7%

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

Alternative 14: 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. *-commutative 99.0%

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

   2. associate-*l/ 99.8%

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

3. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

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

Alternative 15: 48.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-289}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 3.55 \cdot 10^{-273}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+128}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.1e-289)
   (* a 120.0)
   (if (<= x 3.55e-273)
     (* 60.0 (/ y t))
     (if (<= x 8e+128) (* a 120.0) (* -60.0 (/ x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.1e-289) {
		tmp = a * 120.0;
	} else if (x <= 3.55e-273) {
		tmp = 60.0 * (y / t);
	} else if (x <= 8e+128) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.1d-289)) then
        tmp = a * 120.0d0
    else if (x <= 3.55d-273) then
        tmp = 60.0d0 * (y / t)
    else if (x <= 8d+128) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.1e-289) {
		tmp = a * 120.0;
	} else if (x <= 3.55e-273) {
		tmp = 60.0 * (y / t);
	} else if (x <= 8e+128) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.1e-289:
		tmp = a * 120.0
	elif x <= 3.55e-273:
		tmp = 60.0 * (y / t)
	elif x <= 8e+128:
		tmp = a * 120.0
	else:
		tmp = -60.0 * (x / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.1e-289)
		tmp = Float64(a * 120.0);
	elseif (x <= 3.55e-273)
		tmp = Float64(60.0 * Float64(y / t));
	elseif (x <= 8e+128)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.1e-289)
		tmp = a * 120.0;
	elseif (x <= 3.55e-273)
		tmp = 60.0 * (y / t);
	elseif (x <= 8e+128)
		tmp = a * 120.0;
	else
		tmp = -60.0 * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.1e-289], N[(a * 120.0), $MachinePrecision], If[LessEqual[x, 3.55e-273], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e+128], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1e-289 or 3.54999999999999992e-273 < x < 8.0000000000000006e128

   1. Initial program 98.8%

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

   2. Taylor expanded in z around inf 58.1%

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

   if -1.1e-289 < x < 3.54999999999999992e-273

   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* 99.8%

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

      3. frac-2neg 99.8%

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

      4. distribute-frac-neg 99.8%

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

      5. div-inv 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. metadata-eval 99.8%

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

      8. metadata-eval 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around 0 67.0%

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

      1. *-commutative 67.0%

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

   6. Simplified 67.0%

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

   7. Taylor expanded in y around inf 53.5%

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

   if 8.0000000000000006e128 < x

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.7%

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

      3. frac-2neg 99.7%

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

      4. distribute-frac-neg 99.7%

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

      5. div-inv 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. metadata-eval 99.7%

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

      8. metadata-eval 99.7%

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

   3. Applied egg-rr 99.7%

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

      1. +-commutative 99.7%

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

      2. unsub-neg 99.7%

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

      3. div-inv 99.6%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 99.6%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.8%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 72.3%

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

   7. Taylor expanded in z around 0 49.0%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-289}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 3.55 \cdot 10^{-273}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+128}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]

Alternative 16: 48.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-289}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 3.55 \cdot 10^{-273}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+128}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.1e-289)
   (* a 120.0)
   (if (<= x 3.55e-273)
     (* 60.0 (/ y t))
     (if (<= x 8e+128) (* a 120.0) (/ (* x -60.0) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.1e-289) {
		tmp = a * 120.0;
	} else if (x <= 3.55e-273) {
		tmp = 60.0 * (y / t);
	} else if (x <= 8e+128) {
		tmp = a * 120.0;
	} else {
		tmp = (x * -60.0) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.1d-289)) then
        tmp = a * 120.0d0
    else if (x <= 3.55d-273) then
        tmp = 60.0d0 * (y / t)
    else if (x <= 8d+128) then
        tmp = a * 120.0d0
    else
        tmp = (x * (-60.0d0)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.1e-289) {
		tmp = a * 120.0;
	} else if (x <= 3.55e-273) {
		tmp = 60.0 * (y / t);
	} else if (x <= 8e+128) {
		tmp = a * 120.0;
	} else {
		tmp = (x * -60.0) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.1e-289:
		tmp = a * 120.0
	elif x <= 3.55e-273:
		tmp = 60.0 * (y / t)
	elif x <= 8e+128:
		tmp = a * 120.0
	else:
		tmp = (x * -60.0) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.1e-289)
		tmp = Float64(a * 120.0);
	elseif (x <= 3.55e-273)
		tmp = Float64(60.0 * Float64(y / t));
	elseif (x <= 8e+128)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(x * -60.0) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.1e-289)
		tmp = a * 120.0;
	elseif (x <= 3.55e-273)
		tmp = 60.0 * (y / t);
	elseif (x <= 8e+128)
		tmp = a * 120.0;
	else
		tmp = (x * -60.0) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.1e-289], N[(a * 120.0), $MachinePrecision], If[LessEqual[x, 3.55e-273], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e+128], N[(a * 120.0), $MachinePrecision], N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1e-289 or 3.54999999999999992e-273 < x < 8.0000000000000006e128

   1. Initial program 98.8%

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

   2. Taylor expanded in z around inf 58.1%

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

   if -1.1e-289 < x < 3.54999999999999992e-273

   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* 99.8%

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

      3. frac-2neg 99.8%

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

      4. distribute-frac-neg 99.8%

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

      5. div-inv 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. metadata-eval 99.8%

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

      8. metadata-eval 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around 0 67.0%

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

      1. *-commutative 67.0%

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

   6. Simplified 67.0%

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

   7. Taylor expanded in y around inf 53.5%

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

   if 8.0000000000000006e128 < x

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.7%

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

      3. frac-2neg 99.7%

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

      4. distribute-frac-neg 99.7%

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

      5. div-inv 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. metadata-eval 99.7%

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

      8. metadata-eval 99.7%

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

   3. Applied egg-rr 99.7%

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

      1. +-commutative 99.7%

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

      2. unsub-neg 99.7%

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

      3. div-inv 99.6%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 99.6%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.8%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 72.3%

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

   7. Taylor expanded in z around 0 49.0%

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

      1. associate-*r/ 49.0%

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

   9. Simplified 49.0%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-289}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 3.55 \cdot 10^{-273}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+128}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \end{array} \]

Alternative 17: 58.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{-68} \lor \neg \left(a \leq 3.1 \cdot 10^{-54}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.02e-68) (not (<= a 3.1e-54)))
   (* a 120.0)
   (* -60.0 (/ (- x y) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.02e-68) || !(a <= 3.1e-54)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - 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 ((a <= (-1.02d-68)) .or. (.not. (a <= 3.1d-54))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * ((x - 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 ((a <= -1.02e-68) || !(a <= 3.1e-54)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.02e-68) or not (a <= 3.1e-54):
		tmp = a * 120.0
	else:
		tmp = -60.0 * ((x - y) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.02e-68) || !(a <= 3.1e-54))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.02e-68) || ~((a <= 3.1e-54)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * ((x - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.02e-68], N[Not[LessEqual[a, 3.1e-54]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.01999999999999997e-68 or 3.10000000000000004e-54 < a

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf 70.2%

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

   if -1.01999999999999997e-68 < a < 3.10000000000000004e-54

   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%

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

      2. fma-def 98.7%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around 0 86.5%

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

   7. Taylor expanded in z around 0 45.9%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{-68} \lor \neg \left(a \leq 3.1 \cdot 10^{-54}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]

Alternative 18: 50.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 7.5 \cdot 10^{+128}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x 7.5e+128) (* a 120.0) (* -60.0 (/ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 7.5e+128) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= 7.5d+128) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 7.5e+128) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 7.5e+128:
		tmp = a * 120.0
	else:
		tmp = -60.0 * (x / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= 7.5e+128)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= 7.5e+128)
		tmp = a * 120.0;
	else
		tmp = -60.0 * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, 7.5e+128], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 7.50000000000000076e128

   1. Initial program 98.9%

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

   2. Taylor expanded in z around inf 55.4%

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

   if 7.50000000000000076e128 < x

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.7%

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

      3. frac-2neg 99.7%

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

      4. distribute-frac-neg 99.7%

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

      5. div-inv 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. metadata-eval 99.7%

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

      8. metadata-eval 99.7%

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

   3. Applied egg-rr 99.7%

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

      1. +-commutative 99.7%

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

      2. unsub-neg 99.7%

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

      3. div-inv 99.6%

         \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot -0.016666666666666666}} \]

      4. *-commutative 99.6%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot \left(z - t\right)}} \]

      5. associate-/r* 99.8%

         \[\leadsto a \cdot 120 - \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{z - t}} \]

      6. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 72.3%

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

   7. Taylor expanded in z around 0 49.0%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7.5 \cdot 10^{+128}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]

Alternative 19: 50.7% 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. Taylor expanded in z around inf 50.3%

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

3. Final simplification 50.3%

   \[\leadsto a \cdot 120 \]

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 2023332 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

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

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