\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\]

↓

\[\begin{array}{l} \mathbf{if}\;t \le -3.51589399745521548 \cdot 10^{199} \lor \neg \left(t \le 3.0407823536229762 \cdot 10^{156}\right):\\ \;\;\;\;\mathsf{fma}\left(t, i \cdot b, -\mathsf{fma}\left(z, b \cdot c, t \cdot \left(x \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(j \cdot \left(c \cdot a\right) + 1 \cdot \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)\right)\right)\\ \end{array}\]

\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)

↓

\begin{array}{l}
\mathbf{if}\;t \le -3.51589399745521548 \cdot 10^{199} \lor \neg \left(t \le 3.0407823536229762 \cdot 10^{156}\right):\\
\;\;\;\;\mathsf{fma}\left(t, i \cdot b, -\mathsf{fma}\left(z, b \cdot c, t \cdot \left(x \cdot a\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(j \cdot \left(c \cdot a\right) + 1 \cdot \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)\right)\right)\\

\end{array}

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r893110 = x;
        double r893111 = y;
        double r893112 = z;
        double r893113 = r893111 * r893112;
        double r893114 = t;
        double r893115 = a;
        double r893116 = r893114 * r893115;
        double r893117 = r893113 - r893116;
        double r893118 = r893110 * r893117;
        double r893119 = b;
        double r893120 = c;
        double r893121 = r893120 * r893112;
        double r893122 = i;
        double r893123 = r893114 * r893122;
        double r893124 = r893121 - r893123;
        double r893125 = r893119 * r893124;
        double r893126 = r893118 - r893125;
        double r893127 = j;
        double r893128 = r893120 * r893115;
        double r893129 = r893111 * r893122;
        double r893130 = r893128 - r893129;
        double r893131 = r893127 * r893130;
        double r893132 = r893126 + r893131;
        return r893132;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r893133 = t;
        double r893134 = -3.5158939974552155e+199;
        bool r893135 = r893133 <= r893134;
        double r893136 = 3.040782353622976e+156;
        bool r893137 = r893133 <= r893136;
        double r893138 = !r893137;
        bool r893139 = r893135 || r893138;
        double r893140 = i;
        double r893141 = b;
        double r893142 = r893140 * r893141;
        double r893143 = z;
        double r893144 = c;
        double r893145 = r893141 * r893144;
        double r893146 = x;
        double r893147 = a;
        double r893148 = r893146 * r893147;
        double r893149 = r893133 * r893148;
        double r893150 = fma(r893143, r893145, r893149);
        double r893151 = -r893150;
        double r893152 = fma(r893133, r893142, r893151);
        double r893153 = y;
        double r893154 = r893153 * r893143;
        double r893155 = r893133 * r893147;
        double r893156 = r893154 - r893155;
        double r893157 = r893146 * r893156;
        double r893158 = r893144 * r893143;
        double r893159 = r893133 * r893140;
        double r893160 = r893158 - r893159;
        double r893161 = r893141 * r893160;
        double r893162 = r893157 - r893161;
        double r893163 = j;
        double r893164 = r893144 * r893147;
        double r893165 = r893163 * r893164;
        double r893166 = 1.0;
        double r893167 = -1.0;
        double r893168 = r893163 * r893153;
        double r893169 = r893140 * r893168;
        double r893170 = r893167 * r893169;
        double r893171 = r893166 * r893170;
        double r893172 = r893165 + r893171;
        double r893173 = r893162 + r893172;
        double r893174 = r893139 ? r893152 : r893173;
        return r893174;
}

Original	12.5
Target	20.3
Herbie	12.0

Derivation

Split input into 2 regimes
if t < -3.5158939974552155e+199 or 3.040782353622976e+156 < t
1. Initial program 24.2
  \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\]
2. Simplified24.2
  \[\leadsto \color{blue}{\mathsf{fma}\left(c \cdot a - y \cdot i, j, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)}\]
3. Taylor expanded around inf 19.8
  \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right) - \left(z \cdot \left(b \cdot c\right) + t \cdot \left(x \cdot a\right)\right)}\]
4. Simplified19.8
  \[\leadsto \color{blue}{\mathsf{fma}\left(t, i \cdot b, -\mathsf{fma}\left(z, b \cdot c, t \cdot \left(x \cdot a\right)\right)\right)}\]
if -3.5158939974552155e+199 < t < 3.040782353622976e+156
1. Initial program 10.7
  \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\]
2. Using strategy rm
3. Applied sub-neg10.7
  \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\]
4. Applied distribute-lft-in10.7
  \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a\right) + j \cdot \left(-y \cdot i\right)\right)}\]
5. Using strategy rm
6. Applied *-un-lft-identity10.7
  \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(j \cdot \left(c \cdot a\right) + \color{blue}{\left(1 \cdot j\right)} \cdot \left(-y \cdot i\right)\right)\]
7. Applied associate-*l*10.7
  \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(j \cdot \left(c \cdot a\right) + \color{blue}{1 \cdot \left(j \cdot \left(-y \cdot i\right)\right)}\right)\]
8. Simplified10.8
  \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(j \cdot \left(c \cdot a\right) + 1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)\right)}\right)\]
Recombined 2 regimes into one program.
Final simplification12.0
\[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3.51589399745521548 \cdot 10^{199} \lor \neg \left(t \le 3.0407823536229762 \cdot 10^{156}\right):\\ \;\;\;\;\mathsf{fma}\left(t, i \cdot b, -\mathsf{fma}\left(z, b \cdot c, t \cdot \left(x \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(j \cdot \left(c \cdot a\right) + 1 \cdot \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))

Error

Target

Derivation

`if t < -3.5158939974552155e+199 or 3.040782353622976e+156 < t`

`if -3.5158939974552155e+199 < t < 3.040782353622976e+156`

Reproduce