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

Percentage Accurate: 99.3% → 99.8%

Time: 5.2s

Alternatives: 22

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--.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. lift--.f64 N/A

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

   5. lower-fma.f64 N/A

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

   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: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{t} \cdot -60\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{-60}{t}, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.1e+23)
   (fma a 120.0 (* (/ (- x y) t) -60.0))
   (if (<= t 8.5e-34)
     (fma (/ (- x y) z) 60.0 (* 120.0 a))
     (fma (- x y) (/ -60.0 t) (* 120.0 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e+23) {
		tmp = fma(a, 120.0, (((x - y) / t) * -60.0));
	} else if (t <= 8.5e-34) {
		tmp = fma(((x - y) / z), 60.0, (120.0 * a));
	} else {
		tmp = fma((x - y), (-60.0 / t), (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.1e+23)
		tmp = fma(a, 120.0, Float64(Float64(Float64(x - y) / t) * -60.0));
	elseif (t <= 8.5e-34)
		tmp = fma(Float64(Float64(x - y) / z), 60.0, Float64(120.0 * a));
	else
		tmp = fma(Float64(x - y), Float64(-60.0 / t), Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.1e+23], N[(a * 120.0 + N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-34], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1000000000000001e23

   1. Initial program 99.5%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 87.6

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

   6. Applied rewrites 87.6%

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

   if -2.1000000000000001e23 < t < 8.5000000000000001e-34

   1. Initial program 99.4%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   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 81.8

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

   4. Applied rewrites 81.8%

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

   if 8.5000000000000001e-34 < t

   1. Initial program 99.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 99.0

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

   3. Applied rewrites 99.0%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-fma.f64 N/A

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

      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 0

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

      1. lower-/.f64 83.8

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

   8. Applied rewrites 83.8%

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

Alternative 4: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{t}\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, t\_1 \cdot -60\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, -60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x y) t)))
   (if (<= t -2.1e+23)
     (fma a 120.0 (* t_1 -60.0))
     (if (<= t 8.5e-34)
       (fma (/ (- x y) z) 60.0 (* 120.0 a))
       (fma t_1 -60.0 (* 120.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) / t;
	double tmp;
	if (t <= -2.1e+23) {
		tmp = fma(a, 120.0, (t_1 * -60.0));
	} else if (t <= 8.5e-34) {
		tmp = fma(((x - y) / z), 60.0, (120.0 * a));
	} else {
		tmp = fma(t_1, -60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) / t)
	tmp = 0.0
	if (t <= -2.1e+23)
		tmp = fma(a, 120.0, Float64(t_1 * -60.0));
	elseif (t <= 8.5e-34)
		tmp = fma(Float64(Float64(x - y) / z), 60.0, Float64(120.0 * a));
	else
		tmp = fma(t_1, -60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -2.1e+23], N[(a * 120.0 + N[(t$95$1 * -60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-34], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1000000000000001e23

   1. Initial program 99.5%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 87.6

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

   6. Applied rewrites 87.6%

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

   if -2.1000000000000001e23 < t < 8.5000000000000001e-34

   1. Initial program 99.4%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   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 81.8

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

   4. Applied rewrites 81.8%

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

   if 8.5000000000000001e-34 < t

   1. Initial program 99.0%

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

   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 83.8

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

   4. Applied rewrites 83.8%

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

Alternative 5: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x y) t) -60.0 (* 120.0 a))))
   (if (<= t -2.1e+23)
     t_1
     (if (<= t 8.5e-34) (fma (/ (- x y) z) 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) / t), -60.0, (120.0 * a));
	double tmp;
	if (t <= -2.1e+23) {
		tmp = t_1;
	} else if (t <= 8.5e-34) {
		tmp = fma(((x - y) / z), 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) / t), -60.0, Float64(120.0 * a))
	tmp = 0.0
	if (t <= -2.1e+23)
		tmp = t_1;
	elseif (t <= 8.5e-34)
		tmp = fma(Float64(Float64(x - y) / z), 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] / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e+23], t$95$1, If[LessEqual[t, 8.5e-34], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1000000000000001e23 or 8.5000000000000001e-34 < t

   1. Initial program 99.2%

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

   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 85.6

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

   4. Applied rewrites 85.6%

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

   if -2.1000000000000001e23 < t < 8.5000000000000001e-34

   1. Initial program 99.4%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   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 81.8

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

   4. Applied rewrites 81.8%

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

Alternative 6: 81.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{z - t}, -60, 120 \cdot a\right)\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{-187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 10^{-81}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y (- z t)) -60.0 (* 120.0 a))))
   (if (<= a -2.9e-187)
     t_1
     (if (<= a 1e-81) (/ (* (- x y) 60.0) (- z t)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / (z - t)), -60.0, (120.0 * a));
	double tmp;
	if (a <= -2.9e-187) {
		tmp = t_1;
	} else if (a <= 1e-81) {
		tmp = ((x - y) * 60.0) / (z - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y / Float64(z - t)), -60.0, Float64(120.0 * a))
	tmp = 0.0
	if (a <= -2.9e-187)
		tmp = t_1;
	elseif (a <= 1e-81)
		tmp = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.9e-187], t$95$1, If[LessEqual[a, 1e-81], N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.89999999999999988e-187 or 9.9999999999999996e-82 < a

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 80.8

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

   4. Applied rewrites 80.8%

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

   if -2.89999999999999988e-187 < a < 9.9999999999999996e-82

   1. Initial program 99.4%

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

   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 83.6

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

   4. Applied rewrites 83.6%

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

Alternative 7: 74.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+55}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-43}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.4e+55)
   (* 120.0 a)
   (if (<= a 7.6e-43) (/ (* (- x y) 60.0) (- z t)) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e+55) {
		tmp = 120.0 * a;
	} else if (a <= 7.6e-43) {
		tmp = ((x - y) * 60.0) / (z - t);
	} 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 <= (-3.4d+55)) then
        tmp = 120.0d0 * a
    else if (a <= 7.6d-43) then
        tmp = ((x - y) * 60.0d0) / (z - t)
    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 <= -3.4e+55) {
		tmp = 120.0 * a;
	} else if (a <= 7.6e-43) {
		tmp = ((x - y) * 60.0) / (z - t);
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.4e+55:
		tmp = 120.0 * a
	elif a <= 7.6e-43:
		tmp = ((x - y) * 60.0) / (z - t)
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.4e+55)
		tmp = Float64(120.0 * a);
	elseif (a <= 7.6e-43)
		tmp = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t));
	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 <= -3.4e+55)
		tmp = 120.0 * a;
	elseif (a <= 7.6e-43)
		tmp = ((x - y) * 60.0) / (z - t);
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.4e+55], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, 7.6e-43], N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.3999999999999998e55 or 7.59999999999999939e-43 < 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 74.8

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

   4. Applied rewrites 74.8%

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

   if -3.3999999999999998e55 < a < 7.59999999999999939e-43

   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 74.1

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

   4. Applied rewrites 74.1%

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

Alternative 8: 74.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+55}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-43}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.4e+55)
   (* 120.0 a)
   (if (<= a 7.6e-43) (* (- x y) (/ 60.0 (- z t))) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e+55) {
		tmp = 120.0 * a;
	} else if (a <= 7.6e-43) {
		tmp = (x - y) * (60.0 / (z - t));
	} 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 <= (-3.4d+55)) then
        tmp = 120.0d0 * a
    else if (a <= 7.6d-43) then
        tmp = (x - y) * (60.0d0 / (z - t))
    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 <= -3.4e+55) {
		tmp = 120.0 * a;
	} else if (a <= 7.6e-43) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.4e+55:
		tmp = 120.0 * a
	elif a <= 7.6e-43:
		tmp = (x - y) * (60.0 / (z - t))
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.4e+55)
		tmp = Float64(120.0 * a);
	elseif (a <= 7.6e-43)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	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 <= -3.4e+55)
		tmp = 120.0 * a;
	elseif (a <= 7.6e-43)
		tmp = (x - y) * (60.0 / (z - t));
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.4e+55], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, 7.6e-43], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.3999999999999998e55 or 7.59999999999999939e-43 < 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 74.8

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

   4. Applied rewrites 74.8%

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

   if -3.3999999999999998e55 < a < 7.59999999999999939e-43

   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 99.3

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

   3. Applied rewrites 99.3%

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

   4. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lift--.f64 74.6

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

   6. Applied rewrites 74.6%

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

Alternative 9: 66.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{t} \cdot 60\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-195}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{z} \cdot 60\right)\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-35}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{z} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{t} \cdot -60\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6e-9)
   (fma a 120.0 (* (/ y t) 60.0))
   (if (<= t 3e-195)
     (fma a 120.0 (* (/ x z) 60.0))
     (if (<= t 4.1e-35)
       (fma a 120.0 (* (/ y z) -60.0))
       (fma a 120.0 (* (/ x t) -60.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6e-9) {
		tmp = fma(a, 120.0, ((y / t) * 60.0));
	} else if (t <= 3e-195) {
		tmp = fma(a, 120.0, ((x / z) * 60.0));
	} else if (t <= 4.1e-35) {
		tmp = fma(a, 120.0, ((y / z) * -60.0));
	} else {
		tmp = fma(a, 120.0, ((x / t) * -60.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6e-9)
		tmp = fma(a, 120.0, Float64(Float64(y / t) * 60.0));
	elseif (t <= 3e-195)
		tmp = fma(a, 120.0, Float64(Float64(x / z) * 60.0));
	elseif (t <= 4.1e-35)
		tmp = fma(a, 120.0, Float64(Float64(y / z) * -60.0));
	else
		tmp = fma(a, 120.0, Float64(Float64(x / t) * -60.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6e-9], N[(a * 120.0 + N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e-195], N[(a * 120.0 + N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.1e-35], N[(a * 120.0 + N[(N[(y / z), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], N[(a * 120.0 + N[(N[(x / t), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.99999999999999996e-9

   1. Initial program 99.5%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 85.9

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

   6. Applied rewrites 85.9%

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

   7. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 71.6

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

   9. Applied rewrites 71.6%

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

   if -5.99999999999999996e-9 < t < 3e-195

   1. Initial program 99.5%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   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 85.6

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

   4. Applied rewrites 85.6%

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

   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 62.7%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 62.7

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

   9. Applied rewrites 62.7%

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

   if 3e-195 < t < 4.10000000000000026e-35

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 66.7

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

   4. Applied rewrites 66.7%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 55.8%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 55.9

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

   9. Applied rewrites 55.9%

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

   if 4.10000000000000026e-35 < t

   1. Initial program 99.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 99.1

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

   3. Applied rewrites 99.1%

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

   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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 83.8

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

   6. Applied rewrites 83.8%

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

   7. Taylor expanded in x around inf

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

      1. lower-/.f64 70.8

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

   9. Applied rewrites 70.8%

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

Alternative 10: 66.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{t} \cdot 60\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-195}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{z} \cdot 60\right)\\ \mathbf{elif}\;t \leq 3700:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{z} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6e-9)
   (fma a 120.0 (* (/ y t) 60.0))
   (if (<= t 3e-195)
     (fma a 120.0 (* (/ x z) 60.0))
     (if (<= t 3700.0)
       (fma a 120.0 (* (/ y z) -60.0))
       (fma (/ y t) 60.0 (* 120.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6e-9) {
		tmp = fma(a, 120.0, ((y / t) * 60.0));
	} else if (t <= 3e-195) {
		tmp = fma(a, 120.0, ((x / z) * 60.0));
	} else if (t <= 3700.0) {
		tmp = fma(a, 120.0, ((y / z) * -60.0));
	} else {
		tmp = fma((y / t), 60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6e-9)
		tmp = fma(a, 120.0, Float64(Float64(y / t) * 60.0));
	elseif (t <= 3e-195)
		tmp = fma(a, 120.0, Float64(Float64(x / z) * 60.0));
	elseif (t <= 3700.0)
		tmp = fma(a, 120.0, Float64(Float64(y / z) * -60.0));
	else
		tmp = fma(Float64(y / t), 60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6e-9], N[(a * 120.0 + N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e-195], N[(a * 120.0 + N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3700.0], N[(a * 120.0 + N[(N[(y / z), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.99999999999999996e-9

   1. Initial program 99.5%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 85.9

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

   6. Applied rewrites 85.9%

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

   7. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 71.6

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

   9. Applied rewrites 71.6%

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

   if -5.99999999999999996e-9 < t < 3e-195

   1. Initial program 99.5%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   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 85.6

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

   4. Applied rewrites 85.6%

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

   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 62.7%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 62.7

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

   9. Applied rewrites 62.7%

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

   if 3e-195 < t < 3700

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 67.5

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

   4. Applied rewrites 67.5%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 55.2%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 55.3

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

   9. Applied rewrites 55.3%

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

   if 3700 < t

   1. Initial program 99.1%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 80.0

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

   4. Applied rewrites 80.0%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift-*.f64 73.1

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

   7. Applied rewrites 73.1%

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

Alternative 11: 66.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-195}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{z} \cdot 60\right)\\ \mathbf{elif}\;t \leq 3700:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{z} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y t) 60.0 (* 120.0 a))))
   (if (<= t -6e-9)
     t_1
     (if (<= t 3e-195)
       (fma a 120.0 (* (/ x z) 60.0))
       (if (<= t 3700.0) (fma a 120.0 (* (/ y z) -60.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / t), 60.0, (120.0 * a));
	double tmp;
	if (t <= -6e-9) {
		tmp = t_1;
	} else if (t <= 3e-195) {
		tmp = fma(a, 120.0, ((x / z) * 60.0));
	} else if (t <= 3700.0) {
		tmp = fma(a, 120.0, ((y / z) * -60.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y / t), 60.0, Float64(120.0 * a))
	tmp = 0.0
	if (t <= -6e-9)
		tmp = t_1;
	elseif (t <= 3e-195)
		tmp = fma(a, 120.0, Float64(Float64(x / z) * 60.0));
	elseif (t <= 3700.0)
		tmp = fma(a, 120.0, Float64(Float64(y / z) * -60.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / t), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e-9], t$95$1, If[LessEqual[t, 3e-195], N[(a * 120.0 + N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3700.0], N[(a * 120.0 + N[(N[(y / z), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.99999999999999996e-9 or 3700 < t

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 79.4

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

   4. Applied rewrites 79.4%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift-*.f64 72.3

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

   7. Applied rewrites 72.3%

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

   if -5.99999999999999996e-9 < t < 3e-195

   1. Initial program 99.5%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   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 85.6

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

   4. Applied rewrites 85.6%

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

   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 62.7%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 62.7

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

   9. Applied rewrites 62.7%

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

   if 3e-195 < t < 3700

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 67.5

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

   4. Applied rewrites 67.5%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 55.2%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 55.3

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

   9. Applied rewrites 55.3%

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

Alternative 12: 66.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right)\\ \mathbf{if}\;t \leq -2.35 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3700:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{z} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y t) 60.0 (* 120.0 a))))
   (if (<= t -2.35e+35)
     t_1
     (if (<= t 3700.0) (fma a 120.0 (* (/ y z) -60.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / t), 60.0, (120.0 * a));
	double tmp;
	if (t <= -2.35e+35) {
		tmp = t_1;
	} else if (t <= 3700.0) {
		tmp = fma(a, 120.0, ((y / z) * -60.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y / t), 60.0, Float64(120.0 * a))
	tmp = 0.0
	if (t <= -2.35e+35)
		tmp = t_1;
	elseif (t <= 3700.0)
		tmp = fma(a, 120.0, Float64(Float64(y / z) * -60.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / t), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.35e+35], t$95$1, If[LessEqual[t, 3700.0], N[(a * 120.0 + N[(N[(y / z), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.35000000000000017e35 or 3700 < t

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 80.1

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

   4. Applied rewrites 80.1%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift-*.f64 73.7

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

   7. Applied rewrites 73.7%

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

   if -2.35000000000000017e35 < t < 3700

   1. Initial program 99.4%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 69.5

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

   4. Applied rewrites 69.5%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 60.3%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 60.4

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

   9. Applied rewrites 60.4%

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

Alternative 13: 59.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+95}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-183}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{-235}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-83}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.2e+95)
   (* 120.0 a)
   (if (<= a -4.3e-183)
     (fma (/ y t) 60.0 (* 120.0 a))
     (if (<= a 2.65e-235)
       (/ (* 60.0 x) (- z t))
       (if (<= a 4.8e-83) (* (/ y (- z t)) -60.0) (* 120.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e+95) {
		tmp = 120.0 * a;
	} else if (a <= -4.3e-183) {
		tmp = fma((y / t), 60.0, (120.0 * a));
	} else if (a <= 2.65e-235) {
		tmp = (60.0 * x) / (z - t);
	} else if (a <= 4.8e-83) {
		tmp = (y / (z - t)) * -60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.2e+95)
		tmp = Float64(120.0 * a);
	elseif (a <= -4.3e-183)
		tmp = fma(Float64(y / t), 60.0, Float64(120.0 * a));
	elseif (a <= 2.65e-235)
		tmp = Float64(Float64(60.0 * x) / Float64(z - t));
	elseif (a <= 4.8e-83)
		tmp = Float64(Float64(y / Float64(z - t)) * -60.0);
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.2e+95], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, -4.3e-183], N[(N[(y / t), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.65e-235], N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e-83], N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.2000000000000006e95 or 4.8000000000000002e-83 < 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 73.1

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

   4. Applied rewrites 73.1%

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

   if -6.2000000000000006e95 < a < -4.30000000000000017e-183

   1. Initial program 99.1%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 69.1

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

   4. Applied rewrites 69.1%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift-*.f64 45.5

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

   7. Applied rewrites 45.5%

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

   if -4.30000000000000017e-183 < a < 2.6500000000000001e-235

   1. Initial program 99.4%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   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 47.4

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

   4. Applied rewrites 47.4%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 47.2

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

   6. Applied rewrites 47.2%

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

   if 2.6500000000000001e-235 < a < 4.8000000000000002e-83

   1. Initial program 99.4%

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

   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 42.0

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

   4. Applied rewrites 42.0%

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

Alternative 14: 58.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-52}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-269}:\\ \;\;\;\;\frac{x - y}{t} \cdot -60\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-83}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.8e-52)
   (* 120.0 a)
   (if (<= a 9.5e-269)
     (* (/ (- x y) t) -60.0)
     (if (<= a 4.8e-83) (* (/ y (- z t)) -60.0) (* 120.0 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.8e-52) {
		tmp = 120.0 * a;
	} else if (a <= 9.5e-269) {
		tmp = ((x - y) / t) * -60.0;
	} else if (a <= 4.8e-83) {
		tmp = (y / (z - t)) * -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 <= (-1.8d-52)) then
        tmp = 120.0d0 * a
    else if (a <= 9.5d-269) then
        tmp = ((x - y) / t) * (-60.0d0)
    else if (a <= 4.8d-83) then
        tmp = (y / (z - t)) * (-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 <= -1.8e-52) {
		tmp = 120.0 * a;
	} else if (a <= 9.5e-269) {
		tmp = ((x - y) / t) * -60.0;
	} else if (a <= 4.8e-83) {
		tmp = (y / (z - t)) * -60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.8e-52:
		tmp = 120.0 * a
	elif a <= 9.5e-269:
		tmp = ((x - y) / t) * -60.0
	elif a <= 4.8e-83:
		tmp = (y / (z - t)) * -60.0
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.8e-52)
		tmp = Float64(120.0 * a);
	elseif (a <= 9.5e-269)
		tmp = Float64(Float64(Float64(x - y) / t) * -60.0);
	elseif (a <= 4.8e-83)
		tmp = Float64(Float64(y / Float64(z - t)) * -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 <= -1.8e-52)
		tmp = 120.0 * a;
	elseif (a <= 9.5e-269)
		tmp = ((x - y) / t) * -60.0;
	elseif (a <= 4.8e-83)
		tmp = (y / (z - t)) * -60.0;
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.8e-52], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, 9.5e-269], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[a, 4.8e-83], N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.79999999999999994e-52 or 4.8000000000000002e-83 < 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

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

      1. lower-*.f64 69.1

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

   4. Applied rewrites 69.1%

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

   if -1.79999999999999994e-52 < a < 9.5000000000000006e-269

   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 99.3

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

   3. Applied rewrites 99.3%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-fma.f64 N/A

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

      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 99.7

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

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 54.6

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

   8. Applied rewrites 54.6%

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

   9. Taylor expanded in t around 0

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lift-/.f64 N/A

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

       4. lift--.f64 44.6

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

   11. Applied rewrites 44.6%

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

   if 9.5000000000000006e-269 < a < 4.8000000000000002e-83

   1. Initial program 99.4%

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

   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 42.7

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

   4. Applied rewrites 42.7%

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

Alternative 15: 58.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-52}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-140}:\\ \;\;\;\;\frac{x - y}{t} \cdot -60\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-82}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.8e-52)
   (* 120.0 a)
   (if (<= a 3.6e-140)
     (* (/ (- x y) t) -60.0)
     (if (<= a 4.6e-82) (* (/ (- 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 <= -1.8e-52) {
		tmp = 120.0 * a;
	} else if (a <= 3.6e-140) {
		tmp = ((x - y) / t) * -60.0;
	} else if (a <= 4.6e-82) {
		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 <= (-1.8d-52)) then
        tmp = 120.0d0 * a
    else if (a <= 3.6d-140) then
        tmp = ((x - y) / t) * (-60.0d0)
    else if (a <= 4.6d-82) 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 <= -1.8e-52) {
		tmp = 120.0 * a;
	} else if (a <= 3.6e-140) {
		tmp = ((x - y) / t) * -60.0;
	} else if (a <= 4.6e-82) {
		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 <= -1.8e-52:
		tmp = 120.0 * a
	elif a <= 3.6e-140:
		tmp = ((x - y) / t) * -60.0
	elif a <= 4.6e-82:
		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 <= -1.8e-52)
		tmp = Float64(120.0 * a);
	elseif (a <= 3.6e-140)
		tmp = Float64(Float64(Float64(x - y) / t) * -60.0);
	elseif (a <= 4.6e-82)
		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 <= -1.8e-52)
		tmp = 120.0 * a;
	elseif (a <= 3.6e-140)
		tmp = ((x - y) / t) * -60.0;
	elseif (a <= 4.6e-82)
		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, -1.8e-52], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, 3.6e-140], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[a, 4.6e-82], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.79999999999999994e-52 or 4.59999999999999994e-82 < 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

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

      1. lower-*.f64 69.2

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

   4. Applied rewrites 69.2%

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

   if -1.79999999999999994e-52 < a < 3.6e-140

   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 99.3

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

   3. Applied rewrites 99.3%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-fma.f64 N/A

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

      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 99.7

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

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 53.6

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

   8. Applied rewrites 53.6%

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

   9. Taylor expanded in t around 0

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lift-/.f64 N/A

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

       4. lift--.f64 44.1

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

   11. Applied rewrites 44.1%

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

   if 3.6e-140 < a < 4.59999999999999994e-82

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   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 57.8

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

   4. Applied rewrites 57.8%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 38.9

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

   7. Applied rewrites 38.9%

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

Alternative 16: 58.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-52}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-87}:\\ \;\;\;\;\frac{x - y}{t} \cdot -60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.8e-52)
   (* 120.0 a)
   (if (<= a 2.75e-87) (* (/ (- x y) t) -60.0) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.8e-52) {
		tmp = 120.0 * a;
	} else if (a <= 2.75e-87) {
		tmp = ((x - y) / t) * -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 <= (-1.8d-52)) then
        tmp = 120.0d0 * a
    else if (a <= 2.75d-87) then
        tmp = ((x - y) / t) * (-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 <= -1.8e-52) {
		tmp = 120.0 * a;
	} else if (a <= 2.75e-87) {
		tmp = ((x - y) / t) * -60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.8e-52:
		tmp = 120.0 * a
	elif a <= 2.75e-87:
		tmp = ((x - y) / t) * -60.0
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.8e-52)
		tmp = Float64(120.0 * a);
	elseif (a <= 2.75e-87)
		tmp = Float64(Float64(Float64(x - y) / t) * -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 <= -1.8e-52)
		tmp = 120.0 * a;
	elseif (a <= 2.75e-87)
		tmp = ((x - y) / t) * -60.0;
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.8e-52], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, 2.75e-87], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.79999999999999994e-52 or 2.7500000000000002e-87 < 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

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

      1. lower-*.f64 69.0

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

   4. Applied rewrites 69.0%

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

   if -1.79999999999999994e-52 < a < 2.7500000000000002e-87

   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 99.3

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

   3. Applied rewrites 99.3%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-fma.f64 N/A

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

      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 99.7

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

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 53.6

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

   8. Applied rewrites 53.6%

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

   9. Taylor expanded in t around 0

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lift-/.f64 N/A

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

       4. lift--.f64 43.2

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

   11. Applied rewrites 43.2%

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

Alternative 17: 54.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+230}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+146}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -2e+230)
     (/ (* 60.0 y) t)
     (if (<= t_1 2e+146) (* 120.0 a) (* (/ x z) 60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+230) {
		tmp = (60.0 * y) / t;
	} else if (t_1 <= 2e+146) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / z) * 60.0;
	}
	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 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-2d+230)) then
        tmp = (60.0d0 * y) / t
    else if (t_1 <= 2d+146) then
        tmp = 120.0d0 * a
    else
        tmp = (x / z) * 60.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+230) {
		tmp = (60.0 * y) / t;
	} else if (t_1 <= 2e+146) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / z) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -2e+230:
		tmp = (60.0 * y) / t
	elif t_1 <= 2e+146:
		tmp = 120.0 * a
	else:
		tmp = (x / z) * 60.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+230)
		tmp = Float64(Float64(60.0 * y) / t);
	elseif (t_1 <= 2e+146)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x / z) * 60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+230)
		tmp = (60.0 * y) / t;
	elseif (t_1 <= 2e+146)
		tmp = 120.0 * a;
	else
		tmp = (x / z) * 60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+230], N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 2e+146], N[(120.0 * a), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000002e230

   1. Initial program 96.4%

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

   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 50.1

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

   4. Applied rewrites 50.1%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 32.4

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

   7. Applied rewrites 32.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 31.9

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

   9. Applied rewrites 31.9%

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

   if -2.0000000000000002e230 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.99999999999999987e146

   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 59.9

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

   4. Applied rewrites 59.9%

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

   if 1.99999999999999987e146 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.1%

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

   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 59.4

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

   4. Applied rewrites 59.4%

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

   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 31.0

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

   7. Applied rewrites 31.0%

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

Alternative 18: 54.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot y}{t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+142}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 y) t)) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -2e+230) t_1 (if (<= t_2 5e+142) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * y) / t;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+230) {
		tmp = t_1;
	} else if (t_2 <= 5e+142) {
		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 = (60.0d0 * y) / t
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-2d+230)) then
        tmp = t_1
    else if (t_2 <= 5d+142) 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 = (60.0 * y) / t;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+230) {
		tmp = t_1;
	} else if (t_2 <= 5e+142) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * y) / t
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -2e+230:
		tmp = t_1
	elif t_2 <= 5e+142:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * y) / t)
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+230)
		tmp = t_1;
	elseif (t_2 <= 5e+142)
		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 = (60.0 * y) / t;
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e+230)
		tmp = t_1;
	elseif (t_2 <= 5e+142)
		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[(60.0 * y), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+230], t$95$1, If[LessEqual[t$95$2, 5e+142], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000002e230 or 5.0000000000000001e142 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.5%

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

   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 47.6

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

   4. Applied rewrites 47.6%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 30.0

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

   7. Applied rewrites 30.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 29.7

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

   9. Applied rewrites 29.7%

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

   if -2.0000000000000002e230 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.0000000000000001e142

   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 60.0

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

   4. Applied rewrites 60.0%

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

Alternative 19: 54.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t} \cdot 60\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+142}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y t) 60.0)) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -2e+230) t_1 (if (<= t_2 5e+142) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / t) * 60.0;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+230) {
		tmp = t_1;
	} else if (t_2 <= 5e+142) {
		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 = (y / t) * 60.0d0
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-2d+230)) then
        tmp = t_1
    else if (t_2 <= 5d+142) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / t) * 60.0;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+230) {
		tmp = t_1;
	} else if (t_2 <= 5e+142) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / t) * 60.0
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -2e+230:
		tmp = t_1
	elif t_2 <= 5e+142:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / t) * 60.0)
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+230)
		tmp = t_1;
	elseif (t_2 <= 5e+142)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / t) * 60.0;
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e+230)
		tmp = t_1;
	elseif (t_2 <= 5e+142)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / 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, -2e+230], t$95$1, If[LessEqual[t$95$2, 5e+142], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000002e230 or 5.0000000000000001e142 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.5%

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

   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 47.6

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

   4. Applied rewrites 47.6%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 30.0

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

   7. Applied rewrites 30.0%

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

   if -2.0000000000000002e230 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.0000000000000001e142

   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 60.0

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

   4. Applied rewrites 60.0%

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

Alternative 20: 54.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+257}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \mathbf{elif}\;t\_1 \leq 10^{+176}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60 \cdot x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -2e+257)
     (* (/ x t) -60.0)
     (if (<= t_1 1e+176) (* 120.0 a) (/ (* -60.0 x) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+257) {
		tmp = (x / t) * -60.0;
	} else if (t_1 <= 1e+176) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 * x) / t;
	}
	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 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-2d+257)) then
        tmp = (x / t) * (-60.0d0)
    else if (t_1 <= 1d+176) then
        tmp = 120.0d0 * a
    else
        tmp = ((-60.0d0) * x) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+257) {
		tmp = (x / t) * -60.0;
	} else if (t_1 <= 1e+176) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 * x) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -2e+257:
		tmp = (x / t) * -60.0
	elif t_1 <= 1e+176:
		tmp = 120.0 * a
	else:
		tmp = (-60.0 * x) / t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+257)
		tmp = Float64(Float64(x / t) * -60.0);
	elseif (t_1 <= 1e+176)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(-60.0 * x) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+257)
		tmp = (x / t) * -60.0;
	elseif (t_1 <= 1e+176)
		tmp = 120.0 * a;
	else
		tmp = (-60.0 * x) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+257], N[(N[(x / t), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+176], N[(120.0 * a), $MachinePrecision], N[(N[(-60.0 * x), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.00000000000000006e257

   1. Initial program 95.5%

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

   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 51.8

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

   4. Applied rewrites 51.8%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 37.1

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

   7. Applied rewrites 37.1%

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

   if -2.00000000000000006e257 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1e176

   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 58.1

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

   4. Applied rewrites 58.1%

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

   if 1e176 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.8%

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

   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 50.2

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

   4. Applied rewrites 50.2%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 32.1

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

   7. Applied rewrites 32.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 31.8

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

   9. Applied rewrites 31.8%

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

Alternative 21: 53.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t} \cdot -60\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+176}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ x t) -60.0)) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -2e+257) t_1 (if (<= t_2 1e+176) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / t) * -60.0;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+257) {
		tmp = t_1;
	} else if (t_2 <= 1e+176) {
		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 / t) * (-60.0d0)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-2d+257)) then
        tmp = t_1
    else if (t_2 <= 1d+176) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / t) * -60.0;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+257) {
		tmp = t_1;
	} else if (t_2 <= 1e+176) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x / t) * -60.0
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -2e+257:
		tmp = t_1
	elif t_2 <= 1e+176:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x / t) * -60.0)
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+257)
		tmp = t_1;
	elseif (t_2 <= 1e+176)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x / t) * -60.0;
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e+257)
		tmp = t_1;
	elseif (t_2 <= 1e+176)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] * -60.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+257], t$95$1, If[LessEqual[t$95$2, 1e+176], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.00000000000000006e257 or 1e176 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.0%

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

   2. 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 50.7

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

   4. Applied rewrites 50.7%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 33.9

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

   7. Applied rewrites 33.9%

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

   if -2.00000000000000006e257 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1e176

   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 58.1

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

   4. Applied rewrites 58.1%

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

Alternative 22: 50.0% 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 50.0

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

4. Applied rewrites 50.0%

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

Reproduce

herbie shell --seed 2025106 
(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)))