Linear.Matrix:det44 from linear-1.19.1.3

Average Error: 27.1 → 28.0

Time: 45.1s

Precision: binary64

Math

\[\]

↓

\[\]

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (x * y)) - ((double) (z * t)))) * ((double) (((double) (a * b)) - ((double) (c * i)))))) - ((double) (((double) (((double) (x * j)) - ((double) (z * k)))) * ((double) (((double) (y0 * b)) - ((double) (y1 * i)))))))) + ((double) (((double) (((double) (x * y2)) - ((double) (z * y3)))) * ((double) (((double) (y0 * c)) - ((double) (y1 * a)))))))) + ((double) (((double) (((double) (t * j)) - ((double) (y * k)))) * ((double) (((double) (y4 * b)) - ((double) (y5 * i)))))))) - ((double) (((double) (((double) (t * y2)) - ((double) (y * y3)))) * ((double) (((double) (y4 * c)) - ((double) (y5 * a)))))))) + ((double) (((double) (((double) (k * y2)) - ((double) (j * y3)))) * ((double) (((double) (y4 * y1)) - ((double) (y5 * y0))))))));
}

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double VAR;
	if ((j <= -2.1818467664147247e+72)) {
		VAR = ((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (x * y)) - ((double) (z * t)))) * ((double) (((double) (a * b)) - ((double) (c * i)))))) + ((double) (((double) (((double) (j * x)) - ((double) (z * k)))) * ((double) (((double) (i * y1)) - ((double) (b * y0)))))))) + ((double) (((double) (((double) (x * y2)) - ((double) (z * y3)))) * ((double) (((double) (c * y0)) - ((double) (a * y1)))))))) + ((double) (((double) (((double) (j * t)) - ((double) (y * k)))) * ((double) (((double) (b * y4)) - ((double) (i * y5)))))))) + ((double) (((double) (((double) (y * ((double) (y4 * ((double) (c * y3)))))) + ((double) (y5 * ((double) (t * ((double) (a * y2)))))))) - ((double) (a * ((double) (y * ((double) (y3 * y5)))))))))) + ((double) (((double) (((double) (k * y2)) - ((double) (j * y3)))) * ((double) (((double) (y1 * y4)) - ((double) (y0 * y5))))))));
	} else {
		double VAR_1;
		if ((j <= -1.3166900170414862e-127)) {
			VAR_1 = ((double) (((double) (((double) (((double) (k * y2)) - ((double) (j * y3)))) * ((double) (((double) (y1 * y4)) - ((double) (y0 * y5)))))) + ((double) (((double) (((double) (((double) (((double) (j * t)) - ((double) (y * k)))) * ((double) (((double) (b * y4)) - ((double) (i * y5)))))) + ((double) (((double) (((double) (((double) (x * y2)) - ((double) (z * y3)))) * ((double) (((double) (c * y0)) - ((double) (a * y1)))))) + ((double) (((double) (((double) (t * ((double) (i * ((double) (z * c)))))) - ((double) (((double) (i * ((double) (y * ((double) (x * c)))))) + ((double) (t * ((double) (a * ((double) (z * b)))))))))) + ((double) (((double) (((double) (j * x)) - ((double) (z * k)))) * ((double) (((double) (i * y1)) - ((double) (b * y0)))))))))))) + ((double) (((double) (((double) (t * y2)) - ((double) (y * y3)))) * ((double) (((double) (a * y5)) - ((double) (c * y4))))))))));
		} else {
			double VAR_2;
			if ((j <= 4.193679490867568e-213)) {
				VAR_2 = ((double) (((double) (((double) (((double) (k * y2)) - ((double) (j * y3)))) * ((double) (((double) (y1 * y4)) - ((double) (y0 * y5)))))) + ((double) (((double) (((double) (((double) (((double) (((double) (((double) (x * y)) - ((double) (z * t)))) * ((double) (((double) (a * b)) - ((double) (c * i)))))) + ((double) (((double) (((double) (j * x)) - ((double) (z * k)))) * ((double) (((double) (i * y1)) - ((double) (b * y0)))))))) + ((double) (((double) (((double) (x * y2)) - ((double) (z * y3)))) * ((double) (((double) (c * y0)) - ((double) (a * y1)))))))) + ((double) (((double) (b * ((double) (((double) (((double) (j * t)) - ((double) (y * k)))) * y4)))) + ((double) (((double) (i * y5)) * ((double) (((double) (y * k)) - ((double) (j * t)))))))))) + ((double) (((double) (y5 * ((double) (a * ((double) (((double) (t * y2)) - ((double) (y * y3)))))))) + ((double) (c * ((double) (y4 * ((double) (((double) (y * y3)) - ((double) (t * y2))))))))))))));
			} else {
				double VAR_3;
				if ((j <= 1.4388562203440466e-86)) {
					VAR_3 = ((double) (((double) (((double) (((double) (((double) (((double) (j * t)) - ((double) (y * k)))) * ((double) (((double) (b * y4)) - ((double) (i * y5)))))) + ((double) (((double) (((double) (((double) (x * y2)) - ((double) (z * y3)))) * ((double) (((double) (c * y0)) - ((double) (a * y1)))))) + ((double) (((double) (((double) (((double) (x * y)) - ((double) (z * t)))) * ((double) (((double) (a * b)) - ((double) (c * i)))))) + ((double) (((double) (((double) (((double) (j * x)) - ((double) (z * k)))) * ((double) (i * y1)))) + ((double) (b * ((double) (y0 * ((double) (((double) (z * k)) - ((double) (j * x)))))))))))))))) + ((double) (((double) (((double) (t * y2)) - ((double) (y * y3)))) * ((double) (((double) (a * y5)) - ((double) (c * y4)))))))) + ((double) (((double) (y4 * ((double) (y1 * ((double) (((double) (k * y2)) - ((double) (j * y3)))))))) + ((double) (y5 * ((double) (y0 * ((double) (((double) (j * y3)) - ((double) (k * y2))))))))))));
				} else {
					double VAR_4;
					if ((j <= 8.390501765440556e+95)) {
						VAR_4 = ((double) (((double) (((double) (((double) (k * y2)) - ((double) (j * y3)))) * ((double) (((double) (y1 * y4)) - ((double) (y0 * y5)))))) + ((double) (((double) (((double) (((double) (((double) (j * t)) - ((double) (y * k)))) * ((double) (((double) (b * y4)) - ((double) (i * y5)))))) + ((double) (((double) (((double) (((double) (x * y2)) - ((double) (z * y3)))) * ((double) (((double) (c * y0)) - ((double) (a * y1)))))) + ((double) (((double) (((double) (t * ((double) (i * ((double) (z * c)))))) - ((double) (((double) (i * ((double) (y * ((double) (x * c)))))) + ((double) (t * ((double) (a * ((double) (z * b)))))))))) + ((double) (((double) (((double) (j * x)) - ((double) (z * k)))) * ((double) (((double) (i * y1)) - ((double) (b * y0)))))))))))) + ((double) (((double) (((double) (t * y2)) - ((double) (y * y3)))) * ((double) (((double) (a * y5)) - ((double) (c * y4))))))))));
					} else {
						VAR_4 = ((double) (((double) (((double) (((double) (k * y2)) - ((double) (j * y3)))) * ((double) (((double) (y1 * y4)) - ((double) (y0 * y5)))))) + ((double) (((double) (((double) (((double) (((double) (j * t)) - ((double) (y * k)))) * ((double) (((double) (b * y4)) - ((double) (i * y5)))))) + ((double) (((double) (((double) (((double) (x * y2)) - ((double) (z * y3)))) * ((double) (((double) (c * y0)) - ((double) (a * y1)))))) + ((double) (((double) (((double) (((double) (x * y)) - ((double) (z * t)))) * ((double) (((double) (a * b)) - ((double) (c * i)))))) + ((double) (((double) (((double) (j * ((double) (i * ((double) (x * y1)))))) + ((double) (z * ((double) (y0 * ((double) (b * k)))))))) - ((double) (k * ((double) (i * ((double) (z * y1)))))))))))))) + ((double) (((double) (((double) (t * y2)) - ((double) (y * y3)))) * ((double) (((double) (a * y5)) - ((double) (c * y4))))))))));
					}
					VAR_3 = VAR_4;
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Bits error versus j

Bits error versus k

Bits error versus y0

Bits error versus y1

Bits error versus y2

Bits error versus y3

Bits error versus y4

Bits error versus y5

Target

Original	27.1
Target	31.1
Herbie	28.0

\[\]

Derivation

1. Split input into 5 regimes

2. if j < -2.1818467664147247e72

   1. Initial program 31.4

      \[\]

   2. Taylor expanded around inf 32.3

      \[\leadsto \]

   3. Simplified 32.5

      \[\leadsto \]

   if -2.1818467664147247e72 < j < -1.31669001704148622e-127 or 1.4388562203440466e-86 < j < 8.3905017654405557e95

   1. Initial program 24.9

      \[\]

   2. Taylor expanded around inf 27.0

      \[\leadsto \]

   3. Simplified 26.7

      \[\leadsto \]

   if -1.31669001704148622e-127 < j < 4.1936794908675677e-213

   1. Initial program 26.6

      \[\]
   2. Using strategy rm

   3. Applied sub-neg 26.6

      \[\leadsto \]

   4. Applied distribute-lft-in 26.6

      \[\leadsto \]

   5. Simplified 26.6

      \[\leadsto \]
   6. Using strategy rm

   7. Applied associate-*r* 25.9

      \[\leadsto \]
   8. Using strategy rm

   9. Applied sub-neg 25.9

      \[\leadsto \]

   10. Applied distribute-lft-in 25.9

       \[\leadsto \]

   11. Simplified 26.5

       \[\leadsto \]

   12. Simplified 26.6

       \[\leadsto \]

   if 4.1936794908675677e-213 < j < 1.4388562203440466e-86

   1. Initial program 26.2

      \[\]
   2. Using strategy rm

   3. Applied sub-neg 26.2

      \[\leadsto \]

   4. Applied distribute-lft-in 26.2

      \[\leadsto \]

   5. Simplified 25.7

      \[\leadsto \]

   6. Simplified 25.7

      \[\leadsto \]
   7. Using strategy rm

   8. Applied sub-neg 25.7

      \[\leadsto \]

   9. Applied distribute-lft-in 25.7

      \[\leadsto \]

   10. Simplified 25.8

       \[\leadsto \]

   11. Simplified 25.4

       \[\leadsto \]

   if 8.3905017654405557e95 < j

   1. Initial program 31.9

      \[\]

   2. Taylor expanded around inf 36.3

      \[\leadsto \]

   3. Simplified 34.5

      \[\leadsto \]
3. Recombined 5 regimes into one program.

4. Final simplification 28.0

   \[\leadsto \]

Reproduce

herbie shell --seed 2020190 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< y4 -7.206256231996481e+60) (- (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))))) (- (/ (- (* y2 t) (* y3 y)) (/ 1.0 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3.364603505246317e-66) (+ (- (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x))) (* (- (* b y0) (* i y1)) (- (* j x) (* k z)))) (- (* (- (* y0 c) (* a y1)) (- (* x y2) (* z y3))) (- (* (- (* t y2) (* y y3)) (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) (- (* k y2) (* j y3)))))) (if (< y4 -1.2000065055686116e-105) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 6.718963124057495e-279) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (if (< y4 4.77962681403792e-222) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 2.2852241541266835e-175) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (- (* k (* i (* z y1))) (+ (* j (* i (* x y1))) (* y0 (* k (* z b)))))) (- (* z (* y3 (* a y1))) (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3)))))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))))))))

  (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i)))) (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a)))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))