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

Percentage Accurate: 99.3% → 99.8%

Time: 5.0s

Alternatives: 15

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. lift-*.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift-/.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. lift--.f64 N/A

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

   7. +-commutative N/A

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

   8. lower-fma.f64 N/A

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

   9. lower-/.f64 N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 N/A

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

   12. lift--.f64 N/A

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

   13. lift--.f64 99.4

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

3. Applied rewrites 99.4%

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

   1. lift-fma.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift--.f64 N/A

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

   6. +-commutative N/A

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

   7. associate-/l* N/A

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

   8. metadata-eval N/A

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

   9. associate-*r/ N/A

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

   10. *-commutative N/A

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

   11. lower-fma.f64 N/A

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

   12. lift--.f64 N/A

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

   13. associate-*r/ N/A

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

   14. metadata-eval N/A

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

   15. lower-/.f64 N/A

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

   16. lift--.f64 N/A

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

   17. lift-*.f64 99.8

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

5. Applied rewrites 99.8%

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

Alternative 2: 99.4% accurate, 1.0× speedup

Math

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

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(Float64(x - y) * 60.0) / Float64(z - t)))
end

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. lift-*.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift-/.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. lift--.f64 N/A

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

   7. +-commutative N/A

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

   8. lower-fma.f64 N/A

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

   9. lower-/.f64 N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 N/A

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

   12. lift--.f64 N/A

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

   13. lift--.f64 99.4

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

3. Applied rewrites 99.4%

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

Alternative 3: 83.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.000115:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{60}{z}, 120 \cdot a\right)\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-113}:\\ \;\;\;\;\frac{x}{z - t} \cdot 60 + a \cdot 120\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-101}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{t} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.000115)
   (fma (- x y) (/ 60.0 z) (* 120.0 a))
   (if (<= z -1.02e-113)
     (+ (* (/ x (- z t)) 60.0) (* a 120.0))
     (if (<= z 9.2e-101)
       (fma a 120.0 (* (/ (- x y) t) -60.0))
       (fma (/ (- x y) z) 60.0 (* 120.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.000115) {
		tmp = fma((x - y), (60.0 / z), (120.0 * a));
	} else if (z <= -1.02e-113) {
		tmp = ((x / (z - t)) * 60.0) + (a * 120.0);
	} else if (z <= 9.2e-101) {
		tmp = fma(a, 120.0, (((x - y) / t) * -60.0));
	} else {
		tmp = fma(((x - y) / z), 60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.000115)
		tmp = fma(Float64(x - y), Float64(60.0 / z), Float64(120.0 * a));
	elseif (z <= -1.02e-113)
		tmp = Float64(Float64(Float64(x / Float64(z - t)) * 60.0) + Float64(a * 120.0));
	elseif (z <= 9.2e-101)
		tmp = fma(a, 120.0, Float64(Float64(Float64(x - y) / t) * -60.0));
	else
		tmp = fma(Float64(Float64(x - y) / z), 60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.000115], N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.02e-113], N[(N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-101], N[(a * 120.0 + N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.15e-4

   1. Initial program 99.3%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 99.4

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

   3. Applied rewrites 99.4%

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

      1. lift-fma.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. metadata-eval N/A

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

      9. associate-*r/ N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lift--.f64 N/A

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

      13. associate-*r/ N/A

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

      14. metadata-eval N/A

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

      15. lower-/.f64 N/A

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

      16. lift--.f64 N/A

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

      17. lift-*.f64 99.8

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 86.1%

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

   if -1.15e-4 < z < -1.02e-113

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 71.8

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

   4. Applied rewrites 71.8%

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

   if -1.02e-113 < z < 9.1999999999999998e-101

   1. Initial program 99.4%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 99.5

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

   3. Applied rewrites 99.5%

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

   4. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 88.7

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

   6. Applied rewrites 88.7%

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

   if 9.1999999999999998e-101 < z

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 80.8

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

   4. Applied rewrites 80.8%

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

Alternative 4: 83.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-51}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{60}{z}, 120 \cdot a\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-101}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{t} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9e-51)
   (fma (- x y) (/ 60.0 z) (* 120.0 a))
   (if (<= z 9.2e-101)
     (fma a 120.0 (* (/ (- x y) t) -60.0))
     (fma (/ (- x y) z) 60.0 (* 120.0 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e-51) {
		tmp = fma((x - y), (60.0 / z), (120.0 * a));
	} else if (z <= 9.2e-101) {
		tmp = fma(a, 120.0, (((x - y) / t) * -60.0));
	} else {
		tmp = fma(((x - y) / z), 60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9e-51)
		tmp = fma(Float64(x - y), Float64(60.0 / z), Float64(120.0 * a));
	elseif (z <= 9.2e-101)
		tmp = fma(a, 120.0, Float64(Float64(Float64(x - y) / t) * -60.0));
	else
		tmp = fma(Float64(Float64(x - y) / z), 60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9e-51], N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-101], N[(a * 120.0 + N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.99999999999999948e-51

   1. Initial program 99.3%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 99.4

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

   3. Applied rewrites 99.4%

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

      1. lift-fma.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. metadata-eval N/A

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

      9. associate-*r/ N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lift--.f64 N/A

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

      13. associate-*r/ N/A

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

      14. metadata-eval N/A

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

      15. lower-/.f64 N/A

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

      16. lift--.f64 N/A

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

      17. lift-*.f64 99.8

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 83.5%

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

   if -8.99999999999999948e-51 < z < 9.1999999999999998e-101

   1. Initial program 99.4%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 99.5

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

   3. Applied rewrites 99.5%

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

   4. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 86.0

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

   6. Applied rewrites 86.0%

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

   if 9.1999999999999998e-101 < z

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 80.8

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

   4. Applied rewrites 80.8%

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

Alternative 5: 83.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-101}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{t} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x y) z) 60.0 (* 120.0 a))))
   (if (<= z -9e-51)
     t_1
     (if (<= z 9.2e-101) (fma a 120.0 (* (/ (- x y) t) -60.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((x - y) / z), 60.0, (120.0 * a));
	double tmp;
	if (z <= -9e-51) {
		tmp = t_1;
	} else if (z <= 9.2e-101) {
		tmp = fma(a, 120.0, (((x - y) / t) * -60.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(x - y) / z), 60.0, Float64(120.0 * a))
	tmp = 0.0
	if (z <= -9e-51)
		tmp = t_1;
	elseif (z <= 9.2e-101)
		tmp = fma(a, 120.0, Float64(Float64(Float64(x - y) / t) * -60.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e-51], t$95$1, If[LessEqual[z, 9.2e-101], N[(a * 120.0 + N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999948e-51 or 9.1999999999999998e-101 < z

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 82.1

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

   4. Applied rewrites 82.1%

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

   if -8.99999999999999948e-51 < z < 9.1999999999999998e-101

   1. Initial program 99.4%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 99.5

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

   3. Applied rewrites 99.5%

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

   4. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 86.0

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

   6. Applied rewrites 86.0%

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

Alternative 6: 83.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-101}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x y) z) 60.0 (* 120.0 a))))
   (if (<= z -9e-51)
     t_1
     (if (<= z 9.2e-101) (fma (/ (- x y) t) -60.0 (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((x - y) / z), 60.0, (120.0 * a));
	double tmp;
	if (z <= -9e-51) {
		tmp = t_1;
	} else if (z <= 9.2e-101) {
		tmp = fma(((x - y) / t), -60.0, (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(x - y) / z), 60.0, Float64(120.0 * a))
	tmp = 0.0
	if (z <= -9e-51)
		tmp = t_1;
	elseif (z <= 9.2e-101)
		tmp = fma(Float64(Float64(x - y) / t), -60.0, Float64(120.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e-51], t$95$1, If[LessEqual[z, 9.2e-101], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999948e-51 or 9.1999999999999998e-101 < z

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 82.1

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

   4. Applied rewrites 82.1%

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

   if -8.99999999999999948e-51 < z < 9.1999999999999998e-101

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 85.9

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

   4. Applied rewrites 85.9%

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

Alternative 7: 76.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{z}, 60, 120 \cdot a\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-66}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ x z) 60.0 (* 120.0 a))))
   (if (<= z -1.85e-50)
     t_1
     (if (<= z 1.7e-66) (fma (/ (- x y) t) -60.0 (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x / z), 60.0, (120.0 * a));
	double tmp;
	if (z <= -1.85e-50) {
		tmp = t_1;
	} else if (z <= 1.7e-66) {
		tmp = fma(((x - y) / t), -60.0, (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x / z), 60.0, Float64(120.0 * a))
	tmp = 0.0
	if (z <= -1.85e-50)
		tmp = t_1;
	elseif (z <= 1.7e-66)
		tmp = fma(Float64(Float64(x - y) / t), -60.0, Float64(120.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.85e-50], t$95$1, If[LessEqual[z, 1.7e-66], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85e-50 or 1.69999999999999999e-66 < z

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 83.5

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

   4. Applied rewrites 83.5%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 69.9%

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

   if -1.85e-50 < z < 1.69999999999999999e-66

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 84.9

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

   4. Applied rewrites 84.9%

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

Alternative 8: 73.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -66000000:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{-81}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{+71}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z}, -60, a \cdot 120\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -66000000.0)
   (* 120.0 a)
   (if (<= a 1.26e-81)
     (* (- x y) (/ 60.0 (- z t)))
     (if (<= a 2.05e+71)
       (fma (/ x z) 60.0 (* 120.0 a))
       (fma (/ y z) -60.0 (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -66000000.0) {
		tmp = 120.0 * a;
	} else if (a <= 1.26e-81) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if (a <= 2.05e+71) {
		tmp = fma((x / z), 60.0, (120.0 * a));
	} else {
		tmp = fma((y / z), -60.0, (a * 120.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -66000000.0)
		tmp = Float64(120.0 * a);
	elseif (a <= 1.26e-81)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	elseif (a <= 2.05e+71)
		tmp = fma(Float64(x / z), 60.0, Float64(120.0 * a));
	else
		tmp = fma(Float64(y / z), -60.0, Float64(a * 120.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -66000000.0], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, 1.26e-81], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.05e+71], N[(N[(x / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * -60.0 + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.6e7

   1. Initial program 99.5%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 75.7

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

   4. Applied rewrites 75.7%

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

   if -6.6e7 < a < 1.2599999999999999e-81

   1. Initial program 99.3%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 76.6

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

   4. Applied rewrites 76.6%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. lower-*.f64 N/A

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

      9. lift--.f64 N/A

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

      10. associate-*r/ N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 77.0

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

   6. Applied rewrites 77.0%

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

   if 1.2599999999999999e-81 < a < 2.0500000000000001e71

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 60.6

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

   4. Applied rewrites 60.6%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 51.2%

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

   if 2.0500000000000001e71 < 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

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 75.7

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

   4. Applied rewrites 75.7%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 74.7

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

   7. Applied rewrites 74.7%

      \[\leadsto \mathsf{fma}\left(\frac{y}{z}, \color{blue}{-60}, a \cdot 120\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 9: 66.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{z}, 60, 120 \cdot a\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-66}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{t} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ x z) 60.0 (* 120.0 a))))
   (if (<= z -1.5e-50)
     t_1
     (if (<= z 1.7e-66) (fma a 120.0 (* (/ x t) -60.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x / z), 60.0, (120.0 * a));
	double tmp;
	if (z <= -1.5e-50) {
		tmp = t_1;
	} else if (z <= 1.7e-66) {
		tmp = fma(a, 120.0, ((x / t) * -60.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x / z), 60.0, Float64(120.0 * a))
	tmp = 0.0
	if (z <= -1.5e-50)
		tmp = t_1;
	elseif (z <= 1.7e-66)
		tmp = fma(a, 120.0, Float64(Float64(x / t) * -60.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e-50], t$95$1, If[LessEqual[z, 1.7e-66], N[(a * 120.0 + N[(N[(x / t), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.49999999999999995e-50 or 1.69999999999999999e-66 < z

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 83.5

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

   4. Applied rewrites 83.5%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 69.9%

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

   if -1.49999999999999995e-50 < z < 1.69999999999999999e-66

   1. Initial program 99.4%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 69.5

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

   4. Applied rewrites 69.5%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 61.8

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

   7. Applied rewrites 61.8%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 61.8

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

   9. Applied rewrites 61.8%

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

Alternative 10: 60.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.62 \cdot 10^{+208}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+148}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z}, -60, a \cdot 120\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.62e+208)
   (* (/ y (- z t)) -60.0)
   (if (<= y 5.2e+148)
     (fma (/ x z) 60.0 (* 120.0 a))
     (fma (/ y z) -60.0 (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.62e+208) {
		tmp = (y / (z - t)) * -60.0;
	} else if (y <= 5.2e+148) {
		tmp = fma((x / z), 60.0, (120.0 * a));
	} else {
		tmp = fma((y / z), -60.0, (a * 120.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.62e+208)
		tmp = Float64(Float64(y / Float64(z - t)) * -60.0);
	elseif (y <= 5.2e+148)
		tmp = fma(Float64(x / z), 60.0, Float64(120.0 * a));
	else
		tmp = fma(Float64(y / z), -60.0, Float64(a * 120.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.62e+208], N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[y, 5.2e+148], N[(N[(x / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * -60.0 + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.62e208

   1. Initial program 97.2%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 68.6

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

   4. Applied rewrites 68.6%

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

   if -1.62e208 < y < 5.2e148

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 65.1

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

   4. Applied rewrites 65.1%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 60.5%

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

   if 5.2e148 < y

   1. Initial program 98.9%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 56.8

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

   4. Applied rewrites 56.8%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 52.7

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

   7. Applied rewrites 52.7%

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

Alternative 11: 60.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z - t} \cdot 60\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{+198}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.75 \cdot 10^{-36}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+158}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z}, -60, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ x (- z t)) 60.0)))
   (if (<= x -4.6e+198)
     t_1
     (if (<= x -2.75e-36)
       (* 120.0 a)
       (if (<= x 1.9e+158) (fma (/ y z) -60.0 (* a 120.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / (z - t)) * 60.0;
	double tmp;
	if (x <= -4.6e+198) {
		tmp = t_1;
	} else if (x <= -2.75e-36) {
		tmp = 120.0 * a;
	} else if (x <= 1.9e+158) {
		tmp = fma((y / z), -60.0, (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x / Float64(z - t)) * 60.0)
	tmp = 0.0
	if (x <= -4.6e+198)
		tmp = t_1;
	elseif (x <= -2.75e-36)
		tmp = Float64(120.0 * a);
	elseif (x <= 1.9e+158)
		tmp = fma(Float64(y / z), -60.0, Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision]}, If[LessEqual[x, -4.6e+198], t$95$1, If[LessEqual[x, -2.75e-36], N[(120.0 * a), $MachinePrecision], If[LessEqual[x, 1.9e+158], N[(N[(y / z), $MachinePrecision] * -60.0 + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.6000000000000001e198 or 1.8999999999999999e158 < x

   1. Initial program 98.7%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 64.7

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

   4. Applied rewrites 64.7%

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

   if -4.6000000000000001e198 < x < -2.74999999999999992e-36

   1. Initial program 99.4%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 47.6

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

   4. Applied rewrites 47.6%

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

   if -2.74999999999999992e-36 < x < 1.8999999999999999e158

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 66.4

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

   4. Applied rewrites 66.4%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 63.6

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

   7. Applied rewrites 63.6%

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

Alternative 12: 58.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{-122}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-44}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.6e-122)
   (* 120.0 a)
   (if (<= a 7.4e-44) (* (/ (- x y) z) 60.0) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.6e-122) {
		tmp = 120.0 * a;
	} else if (a <= 7.4e-44) {
		tmp = ((x - y) / z) * 60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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 <= (-7.6d-122)) then
        tmp = 120.0d0 * a
    else if (a <= 7.4d-44) then
        tmp = ((x - y) / z) * 60.0d0
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.6e-122) {
		tmp = 120.0 * a;
	} else if (a <= 7.4e-44) {
		tmp = ((x - y) / z) * 60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.6e-122:
		tmp = 120.0 * a
	elif a <= 7.4e-44:
		tmp = ((x - y) / z) * 60.0
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.6e-122)
		tmp = Float64(120.0 * a);
	elseif (a <= 7.4e-44)
		tmp = Float64(Float64(Float64(x - y) / z) * 60.0);
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.6e-122)
		tmp = 120.0 * a;
	elseif (a <= 7.4e-44)
		tmp = ((x - y) / z) * 60.0;
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.6e-122], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, 7.4e-44], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -7.6000000000000002e-122 or 7.4e-44 < a

   1. Initial program 99.4%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 67.0

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

   4. Applied rewrites 67.0%

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

   if -7.6000000000000002e-122 < a < 7.4e-44

   1. Initial program 99.2%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 79.3

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

   4. Applied rewrites 79.3%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 42.0

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

   7. Applied rewrites 42.0%

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

Alternative 13: 57.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{t} \cdot -60\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+305}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+141}:\\ \;\;\;\;\frac{x}{z} \cdot 60\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+166}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ (- x y) t) -60.0)) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -5e+305)
     t_1
     (if (<= t_2 -1e+141)
       (* (/ x z) 60.0)
       (if (<= t_2 4e+166) (* 120.0 a) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) / t) * -60.0;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+305) {
		tmp = t_1;
	} else if (t_2 <= -1e+141) {
		tmp = (x / z) * 60.0;
	} else if (t_2 <= 4e+166) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x - y) / t) * (-60.0d0)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-5d+305)) then
        tmp = t_1
    else if (t_2 <= (-1d+141)) then
        tmp = (x / z) * 60.0d0
    else if (t_2 <= 4d+166) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) / t) * -60.0;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+305) {
		tmp = t_1;
	} else if (t_2 <= -1e+141) {
		tmp = (x / z) * 60.0;
	} else if (t_2 <= 4e+166) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) / t) * -60.0
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -5e+305:
		tmp = t_1
	elif t_2 <= -1e+141:
		tmp = (x / z) * 60.0
	elif t_2 <= 4e+166:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) / t) * -60.0)
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+305)
		tmp = t_1;
	elseif (t_2 <= -1e+141)
		tmp = Float64(Float64(x / z) * 60.0);
	elseif (t_2 <= 4e+166)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) / t) * -60.0;
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+305)
		tmp = t_1;
	elseif (t_2 <= -1e+141)
		tmp = (x / z) * 60.0;
	elseif (t_2 <= 4e+166)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+305], t$95$1, If[LessEqual[t$95$2, -1e+141], N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$2, 4e+166], N[(120.0 * a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.00000000000000009e305 or 3.99999999999999976e166 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 96.8%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 90.2

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

   4. Applied rewrites 90.2%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 58.4

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

   7. Applied rewrites 58.4%

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

   if -5.00000000000000009e305 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.00000000000000002e141

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 50.9

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

   4. Applied rewrites 50.9%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 21.8

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

   7. Applied rewrites 21.8%

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

   if -1.00000000000000002e141 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 3.99999999999999976e166

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 62.5

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

   4. Applied rewrites 62.5%

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

Alternative 14: 52.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot 60\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+218}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ x z) 60.0)))
   (if (<= x -1.3e+205) t_1 (if (<= x 2.3e+218) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / z) * 60.0;
	double tmp;
	if (x <= -1.3e+205) {
		tmp = t_1;
	} else if (x <= 2.3e+218) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) * 60.0d0
    if (x <= (-1.3d+205)) then
        tmp = t_1
    else if (x <= 2.3d+218) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / z) * 60.0;
	double tmp;
	if (x <= -1.3e+205) {
		tmp = t_1;
	} else if (x <= 2.3e+218) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x / z) * 60.0
	tmp = 0
	if x <= -1.3e+205:
		tmp = t_1
	elif x <= 2.3e+218:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x / z) * 60.0)
	tmp = 0.0
	if (x <= -1.3e+205)
		tmp = t_1;
	elseif (x <= 2.3e+218)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x / z) * 60.0;
	tmp = 0.0;
	if (x <= -1.3e+205)
		tmp = t_1;
	elseif (x <= 2.3e+218)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision]}, If[LessEqual[x, -1.3e+205], t$95$1, If[LessEqual[x, 2.3e+218], N[(120.0 * a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2999999999999999e205 or 2.3000000000000001e218 < x

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 57.6

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

   4. Applied rewrites 57.6%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 37.8

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

   7. Applied rewrites 37.8%

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

   if -1.2999999999999999e205 < x < 2.3000000000000001e218

   1. Initial program 99.5%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 54.7

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

   4. Applied rewrites 54.7%

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

Alternative 15: 50.4% accurate, 4.6× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

2. Taylor expanded in z around inf

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

   1. lower-*.f64 50.4

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

4. Applied rewrites 50.4%

   \[\leadsto \color{blue}{120 \cdot a} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025095 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64
  (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))