Average Error: 21.5 → 0.3
Time: 30.5s
Precision: 64
Internal Precision: 320
${\left(\left|x\right|\right)}^2 \cdot {\left(\left|y\right|\right)}^2$
${\left(\left(\left|x\right| \cdot \left|y\right|\right) \cdot \left(\left|x\right| \cdot \left|y\right|\right)\right)}^{1}$

# Derivation

1. Initial program 21.5

${\left(\left|x\right|\right)}^2 \cdot {\left(\left|y\right|\right)}^2$
2. Using strategy rm

$\leadsto {\left(\left|x\right|\right)}^2 \cdot {\color{blue}{\left(\left(\sqrt[3]{\left|y\right|} \cdot \sqrt[3]{\left|y\right|}\right) \cdot \sqrt[3]{\left|y\right|}\right)}}^2$
4. Applied square-prod21.9

$\leadsto {\left(\left|x\right|\right)}^2 \cdot \color{blue}{\left(\left(\left(\sqrt[3]{\left|y\right|} \cdot \sqrt[3]{\left|y\right|}\right) \cdot \left(\sqrt[3]{\left|y\right|} \cdot \sqrt[3]{\left|y\right|}\right)\right) \cdot \left(\sqrt[3]{\left|y\right|} \cdot \sqrt[3]{\left|y\right|}\right)\right)}$
5. Applied associate-*r*17.9

$\leadsto \color{blue}{\left({\left(\left|x\right|\right)}^2 \cdot \left(\left(\sqrt[3]{\left|y\right|} \cdot \sqrt[3]{\left|y\right|}\right) \cdot \left(\sqrt[3]{\left|y\right|} \cdot \sqrt[3]{\left|y\right|}\right)\right)\right) \cdot \left(\sqrt[3]{\left|y\right|} \cdot \sqrt[3]{\left|y\right|}\right)}$
6. Applied simplify3.3

$\leadsto \color{blue}{\left(\left(\left|x\right| \cdot \left|y\right|\right) \cdot \left(\sqrt[3]{\left|y\right|} \cdot \left|x\right|\right)\right)} \cdot \left(\sqrt[3]{\left|y\right|} \cdot \sqrt[3]{\left|y\right|}\right)$
7. Using strategy rm
8. Applied pow13.3

$\leadsto \left(\left(\left|x\right| \cdot \left|y\right|\right) \cdot \left(\sqrt[3]{\left|y\right|} \cdot \left|x\right|\right)\right) \cdot \left(\sqrt[3]{\left|y\right|} \cdot \color{blue}{{\left(\sqrt[3]{\left|y\right|}\right)}^{1}}\right)$
9. Applied pow13.3

$\leadsto \left(\left(\left|x\right| \cdot \left|y\right|\right) \cdot \left(\sqrt[3]{\left|y\right|} \cdot \left|x\right|\right)\right) \cdot \left(\color{blue}{{\left(\sqrt[3]{\left|y\right|}\right)}^{1}} \cdot {\left(\sqrt[3]{\left|y\right|}\right)}^{1}\right)$
10. Applied pow-prod-down3.3

$\leadsto \left(\left(\left|x\right| \cdot \left|y\right|\right) \cdot \left(\sqrt[3]{\left|y\right|} \cdot \left|x\right|\right)\right) \cdot \color{blue}{{\left(\sqrt[3]{\left|y\right|} \cdot \sqrt[3]{\left|y\right|}\right)}^{1}}$
11. Applied pow13.3

$\leadsto \left(\left(\left|x\right| \cdot \left|y\right|\right) \cdot \left(\sqrt[3]{\left|y\right|} \cdot \color{blue}{{\left(\left|x\right|\right)}^{1}}\right)\right) \cdot {\left(\sqrt[3]{\left|y\right|} \cdot \sqrt[3]{\left|y\right|}\right)}^{1}$
12. Applied pow13.3

$\leadsto \left(\left(\left|x\right| \cdot \left|y\right|\right) \cdot \left(\color{blue}{{\left(\sqrt[3]{\left|y\right|}\right)}^{1}} \cdot {\left(\left|x\right|\right)}^{1}\right)\right) \cdot {\left(\sqrt[3]{\left|y\right|} \cdot \sqrt[3]{\left|y\right|}\right)}^{1}$
13. Applied pow-prod-down3.3

$\leadsto \left(\left(\left|x\right| \cdot \left|y\right|\right) \cdot \color{blue}{{\left(\sqrt[3]{\left|y\right|} \cdot \left|x\right|\right)}^{1}}\right) \cdot {\left(\sqrt[3]{\left|y\right|} \cdot \sqrt[3]{\left|y\right|}\right)}^{1}$
14. Applied pow13.3

$\leadsto \left(\left(\left|x\right| \cdot \color{blue}{{\left(\left|y\right|\right)}^{1}}\right) \cdot {\left(\sqrt[3]{\left|y\right|} \cdot \left|x\right|\right)}^{1}\right) \cdot {\left(\sqrt[3]{\left|y\right|} \cdot \sqrt[3]{\left|y\right|}\right)}^{1}$
15. Applied pow13.3

$\leadsto \left(\left(\color{blue}{{\left(\left|x\right|\right)}^{1}} \cdot {\left(\left|y\right|\right)}^{1}\right) \cdot {\left(\sqrt[3]{\left|y\right|} \cdot \left|x\right|\right)}^{1}\right) \cdot {\left(\sqrt[3]{\left|y\right|} \cdot \sqrt[3]{\left|y\right|}\right)}^{1}$
16. Applied pow-prod-down3.3

$\leadsto \left(\color{blue}{{\left(\left|x\right| \cdot \left|y\right|\right)}^{1}} \cdot {\left(\sqrt[3]{\left|y\right|} \cdot \left|x\right|\right)}^{1}\right) \cdot {\left(\sqrt[3]{\left|y\right|} \cdot \sqrt[3]{\left|y\right|}\right)}^{1}$
17. Applied pow-prod-down3.3

$\leadsto \color{blue}{{\left(\left(\left|x\right| \cdot \left|y\right|\right) \cdot \left(\sqrt[3]{\left|y\right|} \cdot \left|x\right|\right)\right)}^{1}} \cdot {\left(\sqrt[3]{\left|y\right|} \cdot \sqrt[3]{\left|y\right|}\right)}^{1}$
18. Applied pow-prod-down3.3

$\leadsto \color{blue}{{\left(\left(\left(\left|x\right| \cdot \left|y\right|\right) \cdot \left(\sqrt[3]{\left|y\right|} \cdot \left|x\right|\right)\right) \cdot \left(\sqrt[3]{\left|y\right|} \cdot \sqrt[3]{\left|y\right|}\right)\right)}^{1}}$
19. Applied simplify0.3

$\leadsto {\color{blue}{\left(\left(\left|x\right| \cdot \left|y\right|\right) \cdot \left(\left|x\right| \cdot \left|y\right|\right)\right)}}^{1}$

# Runtime

Time bar (total: 30.5s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (x y)
:name "sqr(abs(x)) * sqr(abs(y))"
(* (sqr (fabs x)) (sqr (fabs y))))